Estimate the slope of the tangent line of the function f(x)=3ex at the point x=e. slope of the tangent line=

Q: Use the definition of the derivative to find the slope of the tangent line to the graph of the…

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Q: Find the equation of the tangent line to the function f(x)=−3x2−2x at the point where x=1. Give your…

A: Here we find the equation of tangent line of the function fx=-3x2-2xat x =1

Q: Find the slope of the graph of the function at the given point. Use the derivative feature of a…

A: Given :            y = 4(x + 2)2 , (0, 1) To find the slope of the function at the given point.

Q: Differentiate the functions. Find the derivative of y with respect to x. Use the given relation…

A: Given : Function y = x3 + 12   To find : Derivative of the given function dydx?

Q: Use the definition of the derivative to find the slope m of the tangent line to the graph of the…

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Q: Find the equation of the tangent line to the given function at the given value. y = 4x3 + x at x =…

A: Given the equation of the function y=4x3+x At x=-1 the value of y on the given curve is…

Q: Find an equation of the tangent line to the graph of y = f ( x ) at the point on the graph where x…

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Q: Where is the function defined by ƒ(x) = ex increasing?Decreasing? Where is the tangent line…

A: Where is the function defined by ƒ(x) = ex increasing? Decreasing? Where is the tangent line…

Q: Find the derivative of the function. y%3=

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Q: . Find the equation of a line tangent to the graph of f (x) = cotx at x = T/4. .Find the derivative…

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Q: use logarithmic differentiation or the method to find the derivative of y with respect to the given…

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Q: Find the indicated derivative. Then find an equation of the tangent line at the indicated point on…

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Q: Find the second derivative of the function.

A: Given: fx=x cosx Now to find the derivative of the given function, Differentiate given function with…

Q: Find the derivative of the function. y- tan-(V-8

A: In this question, we need to calculate the derivative of the given function.

Q: Identify the equation of the tangent line of the function: f(x) = 3x at x=2

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Q: 6. Find the derivative of f(x) = x² – 3x. Use the result to find the slope of the tangent line to…

A: By using differentiation. and definition of tangent at point.

Q: a) Find the derivative of the function using limits: f (x) = 2x+1 b) Find an equation of the tangent…

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Q: a. First compute the Derivative of f(x) = x and then use it to find the slope of the tangent line to…

A: Equation of Tangent to a curve: Let y=f(x) be the equation of a curve. Then the equation of tangent…

Q: Match the graph of the function with the graph of its derivative.

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Q: 3e* at the point Estimate the slope of the tangent line of the function f(x) x=e (Use decimal…

A: Firstly, we find derivative of f(x) by using the result that derivative of e^x with respect to x  is…

Q: calculate the derivative y = sech x coth x

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Q: Use the definition of derivative (do NOT use the short cut method) to find f'(x) given that f(x) =…

A: Since you have asked  multiple questions in single request  so we  will be answering only first…

Q: Find derivative of f ( x ) = x^3 e^x The slope (rounded to whole number) of the tangent line at x=2…

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Q: Find the slope of the graph of the function at the given point. Use the derivative feature of…

A: The slope of tangent to a curve y=fx  at point a,b is given by dydxx=a.

Q: What is the derivative of a constant function?

A: The derivative of constant function is always zero.

Q: Explain the relationship between the slope and the derivative of ƒ(x) at x = a.

A: Given function is  fx at x=a

Q: Estimate the derivative of the function f (x) = - – 3 at the point x = 3. 3 3 1/5 1/3

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Q: Find the slope of the tangent line of the function g(x)=3-x^2 at the point (2, -1)

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Q: Find the slope of the graph of the function at the given point. y = x-1 y 2.0아 1.5 5. 1.0 0.5 0.5…

A: For slope  of  the curve differentiate w.r.t.x   dydx=ddx1x=-1x2   dydx5/6,6/5=-1x25/6,6/5=m…

Q: Use implicit differentiation to find the slope of the tangent line to the curve 3-x-y – 5-x-y=-2 at…

A: Here we use implicit differentiation to findslope of the tangent line to the curve3xy3-5xy=-2 at the…

Q: Calculate the derivative of the function y=3sinx+2cosx.

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Q: Find the derivative of the cotangent function y=cotx

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Q: Find the derivative of the function y=excosx.

A: we have to find the derivative of the function y=excosx.

Q: Determine the x-values where relative extrema occur for y = (x² +x – 12). Use the second- derivative…

A: Here y=x2+x-122 ⇒y'=ddxx2+x-122       =2x2+x-12ddxx2+x-12       =2x2+x-12(2x+1) for critical points,…

Q: How do you find the derivative of the quotient of two functionsthat are differentiable at a point?

A: Given: Let f and g be two differentiable function at point x.

Q: Find the derivative of f(x)=x2-3x. Use the result to find the slope of the tangent line to the curve…

A: Given: fx=x2-3x To Find: The derivative of the given function and the slope of the tangent line at…

Q: 9. Evaluate the derivative of the function y with respect to x. y = x**

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Q: 1. Describe the relationship between the derivative of a function to the slope of the tangent line.

A: Query- Describe the relationship between the derivative of a function to the slope of the tangent…

Q: Estimate the slope of the tangent line of the function f(x) = 7e* at the point x = e. (Use decimal…

A: We find f'(x)

Q: Determine the points at which the graph of the function has a horizontal tangent line. x² f(x) x-3…

A: Given:      fx=x2x-3 A point on a function will have a horizontal tangent line where the first…

Q: Find the derivztive of the function

A: Topic :- derivative

Q: Find the slope of the tangent line to the graph of the function at the given point. f(x) = 5x - 4x²…

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Q: 14. Find the derivative of the function using the definition of derivative. f (x) = V1 – x

A: Derivatives

Q: y = x-12; (4,) Use the derivative feature of a graphing utility to confirm your results.

A: We will solve the following

Q: find the derivative that function  f(x)=xsinx

A: Given,          fx=xsinx

Q: Use the fact that the derivative of the function f(x) = is f'(x) = - to find the equation of the…

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Q: 8) Using your derivative from the previous question, determine the equation of the tangent line at…

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Q: Find the value of the derivative of the function f (x) = 16 - |x| at the extremum point ( 0, 16)

A: We have to find the value of derivative of the function f(x) = 16 - |x| at the extremum point…

Q: State the notation/symbol for: derivative of y with respect to x derivative of f(x) second…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Estimate the slope of the tangent to the function f(x) = (x + 1)^2(x - 4) at the point of abscissa…

A: Introduction: A tangent line is one that intersects a curve at the so-called point of tangency.…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: