et f(x) = 3 Using Equation (1), find the slope and equation of the ta E x = 2.

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A: Determine the derivative for f(x). fx=lnx5f'x=ddxlnx5=ddx5lnx5×ddxx5=1x5×5x4=5xSo, f'x=5x

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A: Given,           hx=fx2+gx

Q: y = kx xe

A: y=xe-kxTo solve the derivative

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Q: ln(x+(x2 −16)^(1/2)) Find the domain and the derivative of the function.

A: Given, function is

Q: use the method in Example 3 to find (a) the slope of the curve at the given point P, and (b) an…

A: Given, y=2-x3 Point P = (1, 1)

Q: use the method in Example 3 to find (a) the slope of the curve at the given point P, and (b) an…

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Q: Find an equation of the tangent line to the graph of y = g(x) at x = 2 if g(2) = -6 and g'(2) = 4.…

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Q: Find the equation of the tangent line at the point

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Q: The derivative of the function y = tan-1 Vx2 – 1 + csc¬1 x, where x > 1 is: |

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Q: What is the derivative of y=e^x?

A: The derivative of a function y=f(x) gives the rate of change of that function with respect to x.…

Q: d100 y (100th derivatives) dx100 b.y = x100 ; find

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Q: Find an equation of the tangent line to the graph of y = g(x) at x = 3 if g(3) = -2 and g'(3) = 6.…

A: we are given y=g(x),g(3)=-2,g'(3)=6

Q: Vx-1 Find the slope-intercept equation of the tangent line to the graph of at the point x2+1…

A: This question is based on knowing how to calculate slope from a given function at a point.

Q: Using implicit differentiation, for the equation r3+ y³ = 7 is y?

A: Solution is given as below:

Q: b) Find f(1) and find the equation of the tangent line at the point (1, f(1). c) Graph y = f(x) and…

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Q: 4. y=Dx

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Q: Using implicit differentiation, for the equation z° + y° = 9 is

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Q: The point (2,1) is on the graph of x2 . y3 + 5· x² = y² + 23. Find the slope of the line tangent to…

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Q: a. For f(x) =-, find an equation for the secant line through the points where x = 1 and x= 5. b. For…

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Q: Find h'(-3) if h = f o g, f(x) = -8x? + 6 and the equation of the tangent line of g at -3 is y = 7x…

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Q: The derivative of ye* + xe + x + y=0

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Q: Find an equation of the tangent line to the graph of y = g(x) at x = 2 if g(2) = -4 and g'(2) = 5.…

A: Given function is                                              y=g(x), at x=2g(2)=-4 and g'(2)=5 we…

Q: 16. y= 3 cot(n6)

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Q: for the function y = dz -() The derivative dy for the function y= cotV3-2 dz The derivative

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Q: ii) y = e**-2x + x²-e

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Q: 3. A function is defined by the equation y = V3x + 4, where does the slope of the tangent line equal…

A: Given,           A function is defined by the equation y=3x+4 and the slope of the tangent line…

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Q: 21) y=e

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Q: 14. y = a' + cos'r

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Q: Using the properties of derivatives, solve for f"(k lа.

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Q: +++ = 1 find the second derivative y

A: topic - second derivative of a function The given equation is 1x+1y=1 To find the second derivative.

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Q: p>Find the second derivative of f (x) = x*e".

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Q: (a) If F(x) = 5x/(1 + x²), find F'(2) and use it to find an equation of the tangent line to the…

A: Consider the given function as y=5x1+x2