Using the definition of a derivative, find s' (x) given s(x) = -x² – 5x + 8. Provide your answer below: s'(x) =D

Q: Find the derivative of the function.   f(x) = x5 ln(x)   f'(x)=

A: We have to find the derivative of function: fx=x5lnx Here there are two function in multiplication…

Q: find the derivative of the function  f(x) = e5x sec x

A:

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 the 2nd derivative of y with respect to x : y=xe^2x

A:

Q: Find the second derivative for the functions defined as follows g(x) = 4x(ln x)

A: We have to find second derivative of the function: gx=4x lnx Since two function are in product so we…

Q: Find the second derivative for the functions defined as follows.h(x) = x/ex

A: Given:             f(x)=xex

Q: Find the derivative of the function. y = ln(2 − e5x)

A:

Q: B. By using the definition of the derivative, find the for: - dx f(x) = x -

A: Explanation of the answer is as follows

Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: (x2-3x)3 1. у 3 ; d'y/dx

A: Question 1,Given,            y=x2-3x3xTo find : d3ydx3

Q: Use the chain rule to find the derivative of the function z = x2y3 − x along the curve given by x =…

A:

Q: The derivative of f(x) = 5x – Vx + (sin)x – e² -

A: Given; f(x)=5x4-x1/3+[sin(π/2)]x-e2

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

A: Using rules of differentiation.

Q: 5. By calculating a derivative, determine whether the following statement is true (or false): et et…

A:

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

A:

Q: 1 Find the first derivative given that f(x) = xdx +

A:

Q: Find the derivative of f(x) = ln∣cos x∣.

A:

Q: Find the derivative of y with respect to x. 2. y²(x + 2y) = e²

A: Given,

Q: 2. Find the first derivative given that f(x)=x√√x + 1 x²√x

A:

Q: Find the derivative of f (x) = 9ª ln (x).

A: Given: f(x)=9xln(x)

Q: Find the derivative of the function y = ln(9 – e-"). f'(x) =

A: Given that y=ln(9-e-x) To find : Differentiation  y'=f'(x)=ddx(ln(9-e-x))=19-e-xddx(9-e-x)=e-x9-e-x

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

A: Assume z=x^5+1. Then found derivative dy/dx using the chain rule.

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = (x2 ln x)4

A:

Q: Find derivative of f(x) = ln(5x + 2) The slope (as fraction) of the tangent line at x=2 is

A:

Q: Use three-point midpoint formula to evaluate the first derivative of y=x2+5x−1y=x2+5x−1 at x=0x=0…

A: Given function is y=x2+5x−1. We have to evaluate the first derivative of y=x2+5x−1 at x=0 using a…

Q: Compute the derivative: x4 – 4 d - at x = 2 dx x2 – 5 - The derivative is:

A:

Q: 1. x² - 2xy + y² − 6x + 2 = 0

A:

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = ln (t3/2) + √t

A:

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

A:

Q: y = e* - cos 3x + xlog.(1+x)

A: By using some formula of derivative

Q: y = cof'/ x2-1 x²+

A:

Q: Find the derivative of the function. 10 f(x) = + 6cos x Vx

A: Differentiate above equation with respect to x

Q: Find the derivative of the function. f(x) = ln(x − 1)

A:

Q: Find the derivative of the following using the three-step rule 2. y=Va² +x

A:

Q: The derivative of xª at x = e is equal to .Soloot ono

A:

Q: What is the derivative of the function  x^8(ln(x)), and what can I substitute for x to make the…

A: We have to find derivative dy/dx and point where dy/dx =0y is given below:

Q: Find the derivative of the function: f(x)=ln[x^2÷(x+1)^3

A: Formula:

Q: Find the derivative of y with respect to x if y = (5x2 – 10x + 10) e - 6x y' =

A: We have to find the derivative of y with respect to x.

Q: The 60th derivative of x with respect to y of y = x^60 is 60!x

A:

Q: Determine the 8th derivative of y with respect to x of the function : f(x) = 1 / 1 + x2 and find the…

A:

Q: Find the indicated derivative. dz x2 for z = x2 - dx 1- x - 5x2

A:

Q: 8x+9 In(, x3 dx

A: Here we will sove derivative of given function,

Q: What is the first derivative of g(x) = ln #*+1? x2

A: Derivative of ln(x):       ddx(ln(x))=1x Division rule of derivative:-…

Q: Find the derivative of f (x) =arcoth (e³" ).

A:

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

A:

Q: 2. Determine the 8th derivative of y with respect to x of the function f(x) = 1 + x2 and find the…

A: fx=11+x2 Differentiate the above function with respect to x. f'x=ddx11+x2=2x1+x22 Again,…

Q: Find the derivative of V(x) = ln(sin x) – (x4 – 3x)10

A: We can find the derivative as below.

Q: Find the derivative of f(x) = 3/x ln(x), f' (æ) =

A: Chufu