Determine the derivative of the following functions. Show your complete solutions. Factor out the common factors for the final answers if there are any common factors.

Q: Evaluate the derivative of the following functions at the given point  ƒ(r) =π r2; a = 3

A: We first find f'(r) using the exponent rule

Q: ƒ(x) = x0.03 1 f(x) = X0.35

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Q: Find the derivative of the function at the given point (a) by approximating the definition of the…

A: Given: f(x)=x1x   To prove: Find the derivative of the function at the given point (a) by…

Q: Find the derivatives of the following function.

A: Find the derivatives of the following function.

Q: Find the derivative of each function of s = 3t

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Q: Find the derivative of the function. Simplify and express the answer using positive exponents only.…

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Q: 2 y = 3x2

A: Power rule of derivative is defined as dxndx=nxn-1. Difference rule of derivative is defined as…

Q: Find the derivative of the following function. 3 10 -8 y = 5x 2+ 10x i.! y' =O

A: Given: y=5x-32+10x-12+x10-8 We know that ddxxn=nxn-1…

Q: y = V7x – 8

A: Given: y=7x-8 To find:  dy/dx=??

Q: Calculate the derivative of the following functions. y = (x2 + 2x + 7)8

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Q: find the derivative of the following functions

A: Consider the function  g(x)=6x−2xex

Q: Find the derivative of the following function. 9e7x y = 7x-3 y'(x) =O

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Q: Calculate the derivative of the following functions

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Q: 7-4х 3. У 3 5+ 2х

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Q: Calculate the derivative of the following functions

A: Given: y=2x4x-34 for finding derivative first we take log and simplify then differentiate it

Q: Find the derivative of the following function. h(w) = - 12+25 h'(w) =

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Q: Use the product rule to find the derivative of the following function, then select the correct…

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Q: Calculate the derivative of the following functions. #51

A: To evaluate the Derivativey=2ex+3e-x3

Q: Find the derivative respect to x of each of the following functions or equations and simplify:

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Q: Find the derivative of the given function.     y=x^3/5

A: Use power rule to obtain the derivative of given function.

Q: Finally, we factor out the y' and divide, to conclude that the derivative is y'

A: Since it is already solved till part 4 of 5 Therefore, part 5 of 5…

Q: Use a graphing calculator to find ƒ′(2), ƒ′(16), and ƒ′( −3) for the following when the derivative…

A: we have to plot the graph of the given equation and find the value of ƒ′(2), ƒ′(16), and ƒ′( −3) .…

Q: Find the derivatives of the following functions.

A: We have,  y= x3arcCosx3Apply chain rule , y =uv = dudxv +dvdxudydx = d(x3)dxarcCosx3 +darcCosx3dx…

Q: Find the derivative by the definition of each of the following functions: - + 2x

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Q: f(x) = Vx + 1

A: We find derivative of given function

Q: Find the derivative of the function y=x22+x33+x44.

A: Known fact: ddxxn=nxn-1ddxf+g=dfdx+dgdx

Q: find and simplify the derivative of the following function.

A: The given function is h(x)=xexx+1. Product rule: uv'=u'v+v'u Quotient rule: uv'=vu'-uv'v2

Q: Find and simplify the derivative of the following function. f(x) = x+ 15

A: f(x) = x / ( x + 15)  We need to find and simplify the derivative of above given function.

Q: b) f(x) = (e* (Inx² – 3))*

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Q: Calculate the derivatives of the following functions:

A: Product Rule: ddx(f(x)g(x))=g(x)ddx(f(x))+f(x)ddx(g(x)) Chain Rule: ddx(f(g(x)))=ddu(f(u))ddx(g(x))…

Q: Find the derivative of the following: x2 + 3 y = (x – 1)3 + (x + 1)3

A: First of all we will solve the given value of Y then we will differentiate with respect to x

Q: 3. y = Varcsin(1-x²)

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Q: Find the derivative of the following function by first simplifying the expression. 9w-5w f(w) = 4w

A: Given,         fw=9w3-5w4w

Q: Calculate the derivative of the following function. y = 11x- 12

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Q: (b) Find and simplify the derivative of the function f(x) = /

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Q: each

A: We have to find the derivative of the given function using the rule of derivative

Q: Obtain the derivative of the following function, explain each step, and indicate each formula you…

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Q: Calculate the derivative of the following functions

A: Given, y=e2x2x-75 Now by using the product rule, fg'=f'g+g'f Here, f=e2x &…

Q: Find the derivative of the following function: y=x(x2+2)(x3−3).

A: Given function is y=xx2+2x3-3. Power rule of differentiation states that: ddxxn=nxn-1 Product rule…

Q: Find the derivative of the following function. -9e 9x y = 8х - 3 y'(x) =

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Q: Find the derivative of each of the following functions

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Q: c) y = (4x² – 9)(V4x² + 9) csc(x*) d) y = e6x e) y = [sec(2x5 + e15×)][In(4x5)]

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Q: Find the derivative of the following function. 8x +1 h(x) = X +7

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Q: Find the derivative of V 36x

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Q: Calculate the derivative of the following functions. y = (2x6 - 3x3 + 3)5

A: Let y=f(g(x)), by chain rule for differentiation, we have dydx=dfdg·dgdx

Q: 4 b) g(x)=15x* In x

A: Given that, the function is gx=15x4 lnx.