Compute the derivative of the given function in two different ways. x³ + 8x? h(x) = бх? g f' – f • g' g2 a) Use the Quotient Rule, (Fill in each blank, then simplify.) %3D h'(x) = |( )-( ) %3D b) Use algebra first to simplify h, then differentiate without the Quotient Rule. h'(x) =

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y= ln x3

A: Given:

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A: Given: y=sinx2cosx2

Q: Find the derivative of function.

A: Find the derivative of function. y=(ln|x+1|)4

Q: find the derivative of - (z+j)?

A:

Q: Find the derivative of the function. 1-X y arctan, 1+x y'= I3D

A:

Q: Find the derivative of function. y = ln(2 - 5x)

A: we have to find the derivative of y = ln(2 - 5x)

Q: 4. Calculate the derivative of the given function directly from the definition of derivative y = v2x…

A: Given function is  y=√(2x+1)

Q: Compute the derivative using derivative rules. y = 4e -x + 7e -2x

A: Given:     To determine: derivative of the given function

Q: f(x) = Arctan csc² ( 3x

A: Some derivative formulae: ddxtan-1x=11+x2ddxcscx=-cscx cotx Chain rule of derivative:…

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

A:

Q: Find the derative: yain Jx2+4x+1 derivative.

A:

Q: Find the derivative of the functions. y=cosh^-1 (3x)

A: We have to find derivative of the function: y=cosh-13x Rewriting the function, y=cosh-13xcosh y=3x…

Q: y = (cosx)ln*x|

A:

Q: Find the derivative of the function. Express it using positive exponents only. y…

A: For power 3, use the power rule. Then use the chain rule

Q: Find the derivative of the function. rlx) = [in[x*}}°

A:

Q: Find the derivative of: y? – 4x = 0 at point (4,4)

A:

Q: Find the derivative of the cosecant function y=cscx.

A: Given: y=cosecx we know that cosecθ=1sinθ similarly, y=cosecx=1sinx

Q: Compute the derivative of the fo f(x)= 2x+3x ex

A:

Q: Determine the derivative of the given function by using two different methods 2- 3) y = ² + 3

A: Given: y=x2-3x2+34

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

A:

Q: Find the derivative of the function.

A:

Q: Find the second derivative using implicit differentiation of x2+8y2=8

A: Given:

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A: Topic = Derivative

Q: Find the derivative of y given that y= x In x et

A:

Q: Use Leibnitz's Theorem to calculate the 4th derivative of y = x^sin (3x)

A:

Q: Find the first derivative of the function of f(x) using any method?

A: Given,

Q: Find the derivative of y = arctan² (x³)

A: This is a problem of differentiation of the function. Based on general formula we will solve this…

Q: find the derivative of y with respect to x. y= ln3x

A: We can solve the given problem using chain rule derivative.

Q: 1. Y= 3x -x- 2

A: Find your answer below

Q: Find the derivative of flx) = x 1x \ - Does plo) exist

A:

Q: Find the derivative of the function h(x) = x2 arctan5x

A: The given function is h(x) = x2 arctan5x

Q: Find the derivative of ry = -3+x*y° using implicit differentiation.

A:

Q: Find the derivative of y with respect to the appropriate variable. y = cosh12 x+ 5

A:

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = ln3/x

A:

Q: Find the derivative 4 y = In x +

A: It is given that- y=lnx+4x To find the derivative of y, use the addition rule, i.e.,…

Q: Find the derivative of y = csc(V3x² +1

A:

Q: Find the derivative of h(x) = sin2x

A:

Q: 19. Find the derivative of 16 = xy using implicit differentiation.

A:

Q: 3. Find the second derivative using implicit differentiation x² + y? = 4

A: Given that x2+y2=4To find implicit differentiation

Q: use logarithmic differentiation or the method to find the derivative of y with respect to the given…

A:

Q: Use Leibnitz's Theorem to calculate the 4th derivative of y = x+sin(4x)

A:

Q: What is the Derivative of yx

A: f(x) = yx

Q: Find the derivative of the function without using the Quotient Rule. y = -

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Q: find the derivative of y with respect to the appropriatevariable. y = csc-1 x/2

A: We have to find derivative of y with respect to the appropriate variable: y=cosec-1x2 Rewriting the…

Q: use logarithmic differentiation or the method to find the derivative of y with respect to the given…

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Q: Find the derivative of the function y using the increment method or three- step rule. vx +1

A: