Use the derivative to determine whether the function is strictly monotonic on its entire domain and therefore has an inverse function f(x) = 2 − x − x3

Q: Find the derivative of the function by definition 1 1- f(x) = 2x +3

A: Given f(x) = 12x+3 Consider f'(x) = limh→0f(x+h)-f(x)h= limh→012(x+h)+3-12x+3h=…

Q: Find the derivative of the algebraic function.

A: To find the derivative of the algebraic function. f(x)=3x-1x

Q: derivative of the function f (x) = xsec-1 (2x + 1)

A:

Q: Find the derivative of the function using the power rule. (a) f(x) = 3/5x5 − 4x −4/3x-3 (b) f(x) =…

A: a) f(x)=35x5-4x-43x-3 f'(x)=ddx35x5-4x-43x-3       =35ddx1x5-4ddxx-43ddx1x-3…

Q: Use the definition of the derivative to find the derivative of the function f(x) = 3/x and g(x) =…

A: Given f(x) = 3x then f'(x) = limh→0f(x+h)-f(x)h= limh→03x+h-3xh= limh→03x-3x-3hx(x+h)h=…

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: Find the derivative of f(x) = x2√(1 − x2)

A: Given:

Q: Use the Product Rule to find the derivative of the function.

A: Given :           The function h(x) = xx3 + 1 To find the derivative of h(x) using product rule.

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

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Q: Use the Quotient Rule to find the derivative of the function.                           h(x) =…

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Q: Find the derivative of the function. 8x f(x) = In f (x) =

A:

Q: Use the Product Rule to find the derivative of the function. f(x) = x2(2x3 – 1) f'(x) =

A: This is a problem of the derivative of the function. Product rule formula is, UV = U*V' + V*U'…

Q: Find the derivative of the algebraic function.

A: we have to find the derivative of the function f(x)=x41-2x+1

Q: Use derivative rules to find the derivative of h(x) = 3f(x) – 29(x) – x² f (x) + g(z)

A:

Q: Find the derivative of the function. f(x) 1 = - x6 + (x² + 4)(x² – x – 1) + 10

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Q: Use the General Power Rule to find the derivative of the function. g(x) = (9 − 5x)4 g'(x) =

A: Given,

Q: Use the alternate form of the derivative to find the derivative at x-c, if it exists. f(x) = x³ +2x2…

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Q: Use the definition of a derivative to find f'(x) and f"(x). f(x) = 4x² + 7x + 2 f'(x) f"(x)

A:

Q: Use the definition of the derivative to determine the derivative of the following function:  f(x)…

A: Solution by definition of derivative :-

Q: Find the derivative of the function. g(x) = (1 + 5x)5(4 + x – x²)7 - g'(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: Use the Product Rule to find the derivative of the function.

A: The product rule of differentiation is given by: ddxf.g=dfdx.g+f.dgdx The quotient rule of…

Q: Find the derivative of the function. f(x) = (x2 + 3) In(x) f'(x)

A:

Q: Find the derivative of the algebraic function.

A: The given function is fx=x41-2x+1.

Q: Find the derivative of the function. f(x) = x4  (1-(4/x^7)) f '(x) =

A: Given function is Differentiating with respect to x,by using product rule of differentiation, we…

Q: Use the Product Rule or the Quotient Rule to find the derivative of the function.

A: Here we have;  f(x)=x2+x-1x2-1 differentiate with respect to x

Q: Use the formal definition to find the derivative of f(x) = 4 at x = 8. x+3

A: To find the derivative of the function  f(x)=4x+3 at x=8

Q: Use the Product Rule to find the derivative of the function. g(x) = (x2 - 2x + 5)(x³ - 6) g'(x) =

A:

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: Use the formula  to find the derivative of the function

A: Givenf(x)=1x+2To find f'(x)

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

A:

Q: Use the Quotient Rule to find the derivative of the function. 2х — 3 g(x) x - 1 g'(x) = %3D

A: Given that gx=2x-3x2-1

Q: Use the Product Rule to find the derivative of the function. g(x) = (x² – 6x + 7)(x³ – 1) g'(x) =

A:

Q: Use the Quotient Rule to find the derivative of the function. x2 h(x) %D x + 4 h'(x) =

A:

Q: Find the derivative of the function by first expanding or simplifying the expression. f(x) = (5x-…

A: Differentiation of the function with respect to x helps to find the derivative of the function.…

Q: Use the definition of derivative to find f'(x) and f"(x). f(x) = 5x2 + 9x + 2 f'(x) = f"(x)

A:

Q: Find the derivative of the algebraic function.

A: Given algebraic function fx=3x-1x. Differentiating the given function with respect to x,…

Q: Find the derivative of the function. f(x) = 5x4 - x6 f'(x) = %3D

A: The given function is                                   f(x)=5x4-x6 Now we find the derivative of…

Q: Use the Product Rule to find the derivative of the function.                          g(x) = (2x −…

A: Given:gx=2x-31-5x

Q: Find the derivative of the algebraic function.

A: Given, fx=x1-4x+3

Q: Let f(x)=4-1/3x^3. Determine the derivative (f^-1)'(x) of the inverse function to f.

A: Derivative of inverse function is

Q: Use the Generalized Power Rule to find the derivative of the function. f(x) = (3x + 2)5(3x − 2)6

A:

Q: find the derivative of g(x)= sqrt(x) - (2/x^3)

A: In this question we have a function and we have to find the differentiation of that function.…

Q: Use the rules of differentiation to find the derivative of the function             h(x) = 6√x + 3…

A: Our Aim is to differentiate h(x)=6x + 3 x3 -(i)

Q: Find the derivative of f (x)= 2- √(5x) using the definition of derivative.

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Q: Use the General Power Rule to find the derivative of the function. g(x) = V3 - 9x %3D g'(x) =

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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: Use the Product Rule to find the derivative of the function. F(x) = (x³ – 2x)(4x2 + 4x) f '(x) =|

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