Use the formula f(x + h) – f(x) f'(x) = lim %3D h→0 h to find the derivative of the following functions. Then, find the values of the derivatives as specified.

Q: Use the General Power Rule where appropriate to find the derivative of the following functions.

A: We have to find the derivative of the function: y=lnx3+1π We know that lnam=m lna Therefore given…

Q: Find y'(x) from y(z) using the definition of a derivative.

A: according to the problem, we have

Q: Use the Chain Rule to find the derivative. y = sin(x2)

A:

Q: Use the rules for derivatives to find the derivative of function defined as follows. ƒ(x) = e2x…

A: We have to find the derivative of the function: fx=e2xlnxex+1 We know the rule and formula of…

Q: Find the nth-order derivative of the function y=x3sin2x.

A:

Q: Find the derivative y=cos(2x-x^2)

A: Properties used:

Q: Determine the derivative of the following function by applying the quotient rule.…

A: The given function is: h(x)=ln (x2+x)x2+1 The quotient rule for the derivative is given by:…

Q: Use the Chain Rule combined with other differentiation rules to find the derivative of the following…

A: y=ex2+1 sinx3

Q: Find the derivative of h(2) – (, ° ) Assume that a and b are constants.

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Q: Find the derivative with respect to the independent variable. f(x) = cos (- 23x) f'(x) =

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Q: Use the Chain Rule combined with other differentiation rules to find the derivative of the following…

A: Use the Chain Rule combined with other differentiation rules to find the derivative of the following…

Q: Use the quotient rule to find the derivative of the following. x2 - 9x + 1 y% = x2 +2 dy dx

A: See attached file for a step by step explanation.

Q: Compute the derivative using derivative rules.

A: Explanation Given that,  y=(kx+b)-13   Differentiate with respect to x both the sides…

Q: Find the derivative of y with respect to x in the following equation.

A: Using chain rule of differentiation

Q: Find the derivative of the function. y = (tan-1(8x))2

A: Function y=(tan-1(8x)2 To find the derivative of the given function.

Q: Use the alternative form of the derivative to find the derivative at x=c (If it exists)…

A: Given function is fx=x3+3x2+9. We know that, f'x=limx→cfx-fcx-c Given c=-3 Therefore,…

Q: Find the derivative with respect to the independent variable. f(x) = tan (14x) f'(x) =O

A:

Q: Use the alternative form of the derivative to find the derivative at x = c  (if it exists). f(x) =…

A: Definition used -           Alternative form of derivative -…

Q: Find the nth-order derivative of the function y=x2cosx.

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Q: Find the derivative of the following function with respect to x x = sinh2y

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Q: Find the derivative of the following function. f(x) = eax+bx+1,

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Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists. g(x) = 2x2…

A: Given function is gx=2x2-3x. We know that, f'x=limx→cfx-fcx-c Using the above formula of derivative,…

Q: Find the First Derivative of the Given Function: 2.) x=sec53t

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Q: Find the derivative of the function. r(x) = In(x + 1) + 5x7ex r'(x) =

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Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the…

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Q: 1. x + y + xy = 21

A: We will use simple differentiation rules to solve this question.

Q: Use the rules for derivatives to find the derivative of function defined as follows.

A: The given function is: y=ln2x-1x+3 To find the derivative of this function, apply the quotient rule,…

Q: f(x) = x In x

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Q: Find derivatives of the functions defined as follows: y = x2/ex

A: Given function is y=x2ex. To find derivative of the function. Solution: Quotient rule of…

Q: Find the derivative of y with respect to x.

A:

Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists .

A: The derivative of a function fx at x=c is determined using the following alternative form of the…

Q: Use the alternative form of the derivative to find the derivative at x = c (if It exists). f(x) = x2…

A: Given f(x)=x2-2 c=5

Q: 1. x² - 2xy + y² − 6x + 2 = 0

A:

Q: Use the Chain Rule combined with other differentiation rules to find the derivative of the following…

A: Given: y=xx+15 To Find: The derivative of the given function

Q: Find the derivative of the functiony=tan^2(6x)

A: we have to find derivative of f(x)we will use following rules

Q: Find the derivative of f(x) = v3x + 1 using the general formula for differentiation.

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Q: Let y = (x² + 3)'. Use the General Power Rule to find the derivative. y =

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Q: Use the Chain rule with other differentiation rules to find the derivative of the following…

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Q: Find the derivative of the function. f(x) = e In( Vx + 8 f'(x) =

A: Given, f(x) = ex ln(x+8) We have the formulas d(ex)/dx = ex                       ...........(1)…

Q: 2x f{X) = 1+ X

A: Given: f(x)=2x1+x

Q: Find the nth order derivative of the power function y=xm where m is a real number.

A:

Q: Find the derivative with respect to x: y = x3- 3*

A: The given function is: y=x3.3xWe need to find the derivative of y with respect x.Recall the…

Q: Find the derivative of the function. G(x) = V1- 9x2 · arccos(3x) G'(x) =

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Q: Give the derivative formula for the function. (x)2 In x -e j'(x)

A: Consider the given function.

Q: Use the definition of the derivative to find df/dx. f(x) = x/(1-3x)

A: Given, function

Q: Find the derivative using the definition 1- y = vx -1

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Q: Find ☆ f'(x) using using derivative rules. f(x) =Dx+ 2 to 11

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Q: find the derivative of the given function y^4=4xy using implicit differentation

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Q: Find derivatives of the functions defined as follows: y = ex2

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Q: Find the first derivative of v with respect to x

A: Given,