7. Derivative of the Reciprocal Use the limit definition to prove f'(x) 5²(x) d 7. dx (f(x), Hint: Show that the difference quotient for 1/f(x) is equal to f(x) – f(x +h) hf (x)f(x+h)

Q: Find the derivative of the function. Simplify where possible. y = (tan-'x)? y = tan-'(x²) y =…

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Q: Derivative of f(x)=1+ 2x+3xy computed * O explicitly equal to 2+3x implicitly equal to 2+3x+3dy/dx O…

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Q: 3. Approximate the first order derivative of f(x)= x² + 2x at x = 3, using Forward, Backward and…

A: Formulas for differences are enclosed next page

Q: find all relative extrema of thefunction. Use the Second Derivative Test whereapplicable. f(x)=x^{2}…

A: The given function,  f(x) =x2e-x .........................(1)  differentiate with respect to x

Q: Derivative of In |x| Differentiate In x, for x > 0, and differentiate In(-x), for x < 0, to conclude…

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Q: B) Derivative following functions by using chain rule method 1) y = 5u³- u? , 2x = 4u? 2) у %3D |1 ,…

A: Answer (1): Given that, y=5u3-u2, 2x=4u2 Suppose fgx Then, to find the derivative apply the chain…

Q: 2. Using the definition of derivative, prove the following: (a) f= if so)=V (b) y-sec x if y-tanx

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Q: Vrite an equation for the tangent line at x=6 of the curve f(x)=(2x-4) Find the limit using…

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Q: ©if g(x, v) = In(),the )If g(x, y) = Int then xgx - vgw in simplified form is [c].

A: We can find the answer as below in the following steps

Q: 1. Given f (x) = x-Vx gn the interval (0, 9), show work for finding: a. derivative and simplify the…

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Q: 1 Find the derivative of f(x) = - at x= 3 %3D (Type an integer or a simplified fractic 21 %3D

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Q: 10 at x + 4 x = 0 using the limit definition of the derivative. Find the derivative f' (0) of f(x) =

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Q: 8. What rule should be used in deriving f(x) = x³? A. Constant rule B. Sum rule 9. Find dy/dx y=e³x…

A: To find:  8. Name of the rule used in derivative of x5. 9. Derivative of e3x . 10. Derivative of…

Q: Please explain step by step Use the definition to calculate the derivative of the criterion of the…

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Q: All edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the surface…

A: We have to solve above problem.

Q: x 0 entiable at x = 0.

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Q: 2. Using the limit definition of the derivative, find the derivative of the function %3D 2+1 at z =…

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Q: 4. Find the first derivative of the given function using the Rules of Differentiation: sinx 2x-x-1…

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Q: Using limit definition of derivative, prove d/dx e^x=e^x

A: We using limit definition

Q: the derivative of the function f (x) = arccos (1 / x)

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Q: Calculate the first first derivative justifies whether this is differentiable or not. Calculate the…

A: ∴ f(x) = 2x2ex is differentiable

Q: 4. Find the derivative of f(x) = Vr +1 using the limit definition. (a) Find the slope of the tangent…

A: (1) The derivative from the limit definition is:…

Q: equation of tangent line of f(x)=5x^3+1 at x=1 is * O y=15(x-1) O y=15 x-9

A: Given: The function f(x)=5x3+1 and a point x=1

Q: Find the equation of the line tangent to the graph of y = r-2x at the point T= 2. Use the limit…

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Q: Find f'(x) using the limit definition of derivative. Then find f'(1).

A: we have to find derivative of f(x) at x=1  by using limit definition of derivative .definition of…

Q: 3) (a) Let f(x) = -x²-x. Use definition of the derivative Equation 3.4 to compute f'(x). (No other…

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Q: 12. The Definition of the Derivative Find the formula for the instantaneous rate of change of f(x) =…

A: Given:

Q: True of False: Derivative of (arctan(e^(-x^2))) = [-2xe^(-x^2)] / [1 + e^(-2x^2)] Show your…

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Q: Find the value of the derivative (if it exists) at the indicated extremum. f(x) - - 3xVx + 2 10 -2 4…

A: The given function is fx=-3xx+2.

Q: 17. f(x) = x2 + x – 3

A: Answer is f'(x)= 2x+1. Explanation is given below using the limit process....

Q: Compute the derivative of f(x) = ex/ xn for constant n using the specified methods: (a) The…

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Q: 2. Find the derivative of the following function using the definition of derivative. (No credit will…

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Q: 9 f:(-0,0) U (0, ∞) → (∞,0) U (0, ∞0). Where f(x) х Show that f(x) is continuous at x=3 with the…

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Q: 2. Use the definition of derivative (as a limit) to differentiate f(x) the rules of…

A: We need to find derivative using definition of derivative. Definition of derivative is given by -…

Q: Leth(x) = arctan(x2+ 2x). Find all critical values (if any) ofhand use the second derivative test…

A: Explanation of the solution is given below...

Q: se the limit definition of the derivative to find the slope of the tangent line to the curve f ( x )…

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Q: Find the derivative at the given x-value. Show your work! 2n * f(x) = 3 tanx at x = : f(x) = 2 sec x…

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Q: 1. Use centered-difference approximation to estimate the first and second derivatives of y = xex at…

A: Given function is y=f(x)=xexx+1 and h=0.1 O(h2) formulae f'(x)=f(x+h)-f(x-h)2h…

Q: 2. The graph of the derivative function f'(x) of a function f(x) a) Determine: the intervals where…

A: f(x) will be increasing in the range where f'(x) is positive.f(x) is increasing in the range (-∞, 1)…

Q: 5. Calculate the derivative of x* sin (x) showing all your work. 6. Use the limit definition of the…

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

A: The slope of the tangent line of a graph y = f(x) at a point x0 is given by the derivative of…

Q: If f(z) = 2z2 + 6z + 3, find f'(-1), using the definition of derivative. f'(-1) is the limit as z of…

A: We have to find limit and tangent line

Q: True or false: if f is continuous at a, then the derivative of f exists at a. If it is false, can…

A: To find  -- if f is continuous at a, then the derivative of f exists at a or not.

Q: 4. The derivative of f(x) = ln x at x = 3 when hpresent = 0.001 and hprevious = 0.002. %3D 5. The…

A: f(x)=ln…