For the functiony = (x2 + 2)(x3 − 4x),at(−2, 0)find the following.(a) the slope of the tangent line(b) the instantaneous rate of change of the function

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 a power function with the negative exponent y=x−n.

A: We will use the power rule:

Q: Find the derivative of the function. f(x) = ln 3x

A:

Q: By using the definition of the derivative, find the for: - dx 1- f(x) = Vx

A:

Q: Find the derivative of the function f(x) = x√ln x

A: Here given Use the formula of product rule of derivatives as

Q: Find the nth-order derivative of the function y=x3sin2x.

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: Find the derivative gx) = 4 K) = cost dt

A: Problem is solved using Leibniz rule

Q: Find the derivative of y with respect to x if y = (11x2 - 22x+ 22) ex.

A:

Q: What is the derivative of the function f(x)=1/x+1 at x=1?

A: To find out the derivative of the function at x=1

Q: y = ln 1-x² 1+x²

A:

Q: use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = ex−12

A: Given function is y=ex-12. To find the derivative of the given function. Solution: Chain rule of…

Q: By the chain rule, the derivative of arctan (4x^5) is:

A:

Q: Find the derivative of the function. y = (ln x)4

A:

Q: Find the second derivative of function, and then find ƒ″ (1)  and ƒ″ (−3) .

A: Find first the derivative as shown below: f'x=ddx-5-x2        =125-x2ddx5-x2       =-125-x2-2x…

Q: 3. Find the second derivative of y= xlnx

A:

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

A:

Q: what is the derivative of this question with solution y= csc (4x² ) Arccsc (4x² )

A:

Q: Solve for the derivative of y = x(e*) %3D

A: Find your answer below

Q: Find the derivative of the function y = ln 4x / (x − 6)

A:

Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = ex−12

A:

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

A:

Q: Find the derivative of the function. y= log 4- x

A:

Q: For ƒ(x) = ax, find ƒ″(x) and ƒ‴(x). What is the nth derivative of ƒ with respect to x?

A: Since, we have been given that f(x)=ax-(i).Our Aim is to find f"(x) and f'''(x).Also, we have to…

Q: at x: つ:8ー5x, atx=e

A: Given:  F(x) = x3 - 5x ...(1)       and the…

Q: Find the derivative of the function. f(x) = x6 ln(x)

A:

Q: Find the nth order derivative of the square root y=√x.

A: Let's first calculate the nth order derivative of the power function y=xm where m is a real number.

Q: Find the second derivative of the function. g(x) = √x + ex ln x

A: Consider the given function gx=x+ex lnx Now, differentiate the given function with respect to x…

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

A:

Q: Find the derivative   Y=ln(4+X^2 )

A: The given function is,

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 2nd derivative of the function defined implicity by the equation x^1/3+y^1/3=80

A:

Q: n. y= (x+Inx)

A:

Q: 2. If f (x) = xV x + 3, find the derivative of this function and the slope of the tangent line at…

A: Product rule of differentiation: (fg)'=fg'+gf' The slope of a tangent line at (a,b) is given by:…

Q: Find the derivative of the function.

A:

Q: Find the derivative of the function - 3x f(x) = 3 ln(x) + e - df dx

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 derivative of the function g(x) = ln √2x

A:

Q: Find the equation of the line tangent to the graph of the function f(x)=x-2x^2 at x=1 use the…

A: The equation of the curve is: f(x)=x-2x2

Q: Find derivatives of f(x) = {x+- 1 and find the line tangent to it when x = 1

A:

Q: 4. y=ln(4x' +5)

A:

Q: 1. What is the derivative of f(x) = x2 – 8x + 12 when you illustrate using tangent? 2. What is the…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: What is the derivative of the function B(x)=3/(x+2) at x=a?

A:

Q: Find the derivative of the function. h(x) = x² arctan(8x)

A:

Q: 8) Using your derivative from the previous question, determine the equation of the tangent line at…

A:

Q: y = (3x + 4)², solve for y' using derivative of nth power.

A:

Q: Find the 1st derivative of the function: y = 4(Vx + 1)5

A: Given that: y=4(x+1)5

Q: Find the derivative.  y = ln((x + 1)(2x + 9))

A:

Exponential Growth Model

The relation that represents an exponential function is: