For the composite function, identify an inside function and an outside function and write the derivative with respect to x of the composite function. (The function is of the form f(x) = g(h(x)). Use non-identity functions for g(h) and h(x).) f(x) = (3.7x + 5.5)5 {g(h), h(x)} f'"(x) =

Q: Determine the derivative of f(x) = 3 x2 In x with respect to x. f '(x) :

A: We differentiate both sides with respect to x and apply the rule d/dx(uv)=ud/dx(v)+vd/dx(u)

Q: Calculate the derivative of f(x)=4x³ with respect to x and evaluate this derivative at x=2.

A:

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: Find the derivative of the following function using the rules of differentiation: g(x) 3xv1+ x?

A:

Q: By using the First Principle, find the derivative of the following function at x = 2. 4x + 3 f(x) =…

A: We have to find the derivative of f(x)=4x+3x+1 at x=2 by using the First Principle.

Q: 9. Use the definition of derivative to find the derivative of f(x) = x² – 3x.

A: We need to evaluate the derivative of the function f(x) using definition of the following function…

Q: Find derivative of the function f(x)=x power3 -1/x-1

A: By applying the chain rule and quotient rule we find the derivative of a function.

Q: Determine the derivative of f(x) = 3 x² In x with respect to x. f'(x) = |

A: We have to find f'(x)

Q: derivative

A:

Q: Find the derivative of F(x) = 1 / (3x+1) directly from the definition of the derivative:

A: Here the question itself need to use definition of derivative to find out the derivative of given…

Q: Use the following definition of derivative as a function f\x+h}-f(x) f\x)=lim h h --0 To find the…

A: A function is: a relation from a set of inputs to a set of possible outputs where each input is…

Q: Find the derivative of the function. y = In(x8)

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Q: Find the derivative of the function using the definition of derivative. 1 g(x) 8 + Vx g'(x) =

A:

Q: Q1. Find the derivative of f(x) = 2x -- by using the definition of derivative.

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Q: Calculate the derivative of the function below using the quotient rule. 2x ม 5x + 3 f(x) = and g(x)=…

A: Quotient Rule : If  y = f(x)g(x)  then  y' = g(x)·f'(x)-f(x)·g'(x)g(x)2.

Q: Find the derivative of the function g(x) et 5x - g'(x) =

A: We have to use quotient rule for derivative and use  d/dx(ex)=ex d/fx(ax+b)=a

Q: Use the Quotient Rule to find the derivative of the function. h(x) =  x2 x + 7 h'(x) =

A: Consider the provided function:

Q: By using the first principle, find the derivative of the following functions. 1.  f (x) = x^2 - x

A:

Q: Find the derivative of the function f(x) = 8x2 – 13x by the definition of derivatives f(x + h) –…

A: on using this formula we get = 16x-13

Q: Find the derivative of the function using the definition of derivative. 1 f(x) x² - 36

A:

Q: Use the Quotient Rule to find the derivative of the function. x2 h(x) = %3D X + 2 h'(x) =

A:

Q: Given the derivative f'(x), find the x-value for all relative extreme for the graph of the original…

A:

Q: Find the derivative of the function g(x)=x3∫x2tdt.

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Q: Find the derivative using the first principle  F(x)= (x-1)(x-2)

A: Given F(x)=(x-1)(x-2) To find the derivative using the first principle From the first principle, we…

Q: Find the Derivative of the function f by using the rules of differentiation F(x) = x^3+4x^2 + x -4…

A: Power rule:ddxxn=n xn-1ddxx=1

Q: Find the derivative of the function and evaluate the derivative at the given x-value. f(x) = 5x +x…

A:

Q: Use the General Power Rule to find the derivative of the function. g(x) = V2 – 7x g'(x) = %3D

A:

Q: Use the f'(x)=limh->0f(x+h)-f(x)/h  to find the derivative of f(x)=11x2 AT x=1

A:

Q: Find the derivative of the function. f(x) = 4 3√x + 2cos x

A: The given function is ; f(x)=4/3sqrt(x) +2Cosx.

Q: Find the derivative of the function. g(x) = 9 + In(x)

A: We have to find the derivative of : g(x)=ex29+ln(x)

Q: o f(x) = 4~/x+3

A: by using definition of a derivative.

Q: Find the derivative of the function. f(x) = In x+ 2 f'(x) =

A: We have to find the derivative of the given function.

Q: 3. Use the limit definition of the derivative to find the derivative of the function. a) f(x) = 2x²…

A: Given query is to find the derivative using definitely.

Q: Q1. Find the derivative of f(x) = 2x² -- by using the definition of derivative.

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Q: Find the derivative of the function using the definition of derivative. 1 f(x) V5 + x

A:

Q: Given f(x) = ||+x, at which point does the derivative not exist? Mathematically show that the…

A: According to question given that f(x)=|x|+x"A function f is said to be differentiable at a if  f'(a)…

Q: Use the theorems on derivatives to find the derivative of the following function:   f(x) = 3x2cosx +…

A: Given function is  We know that according to product rule of differentiation, we have (uv)'=uv'+vu'

Q: 5. By the General Power Rule, find the derivative of y with respect to x for the function y = (4x5 +…

A: Given that, y=4x5+x4-x33

Q: Find the derivative of the function. g(x) = 2(3- Ex)

A:

Q: Find the derivztive of the function

A: Topic :- derivative

Q: . Use derivative rules to find the derivative of h(x) = 3f(x) – 2g(x) – x² f (x) +. Show steps g(x)

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

Q: Find the derivative of the following function f(x)=2x-1 using the definition of the derivative Show…

A: y=2x-1

Q: Find f (x) of f(x)= by using the definition of the x- derivative.

A: Definition of Derivative is given as

Q: Find the derivative of the following function by definition (from first principle): f(X)=1-x/2x

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Q: function

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Q: Find the derivative of (x+5) / (x2-1) with respect to x.

A: Here we have to use formula of derivative  dxndx=nxn-1

Q: Use the derivative to determine whether the function is strictly monotonic on its entire domain and…

A: The function f(x)=lnx-3. We have to use the derivative to determine whether the function is strictly…

Q: Find the derivative of the function f by using the rules of differentiation. f(x) = (1 + 3x2)2 +…

A: f(x)=(1+3x2)2+4x3 Apply the rule of differentiation  WE apply power rule and chain rule to take…