Let f(x)%3x* Find the value of f'(1). (a) 2 (b) e-1 (c) e (d) e+1 (e) -1

Q: Find the derivative of f(x) = COS 4 log3 (x²) os(5x)

A: Explanation of the answer is as follows

Q: A second derivative Findd2y/dx2 if x2 + y2 = 1.

A:

Q: Find the derivative of f( x ) = 2° log3(z + 2.5) f'(x) =

A: The first derivative of the function is . The product rule of the differentiation is .

Q: What is the average rate of change of the function f(x): = x² between x = -3 and x = 3?

A:

Q: Find the thousandth derivative of  f(x)  = x e-x

A:

Q: 2. Show a graphical method of approximating the instantaneous rate of change at x = 3 for the…

A: You must have idea about what is the basic difference between instantaneous and average rate of…

Q: Estimate the instantaneous rate of change of P(x)=5/x+2 at the point x=2

A:

Q: 2. Determine the second derivative of f(x)= x'e* at x = -2 with a step-size of h=0.50 using Central…

A: Given function is f(x) = x2e2x and h = 0.50

Q: x + x dx x2

A:

Q: If the instantaneous rate of change of ƒ(x) with respect to x is positive when x = 1, is ƒ…

A:

Q: Estimate ln(0.9) using a linear approximation

A: Given:ln(0.9)

Q: 2. Estimate the instantaneous rate of change of y = at x = 1. Show your work. 2x-3x+1

A:

Q: Differentiate f (x) = (ex + e-x)/(ex - e-x)

A: We have to differentiate the function: fx=ex+e-xex-e-x Here two function are in ratio so we need to…

Q: Shows the derivative function of: e3x+5

A:

Q: 14) Find the first derivative of f(x)= 2*2*

A: The derivative of ax is axlna. The derivative of xn is nxn-1, where n is any integer. The chain rule…

Q: Estimate the instantaneous rate of change at the point x=2 for f(x)=ln(x) ROC =

A: the fiven function is f(x)=ln(x)

Q: Find the second derivative of f(x) = x2+ e* - COSX. O a. f(x) = 2x + xex - cosx O b. f'(x) = 2x + e*…

A: Solve by derivative

Q: 1. f(x) =In (ta n"x)

A: Given query is to find the first derivative of the expression.

Q: To investigate these values, we find the second derivative f"(x) = %3D At the positive critical…

A: Given function is : fx=3x-4x3

Q: Find the first derivative of: y = sinh e2" O y e2 cosh e2# 2e2" cosh e2" O y' 2 cosh e2 O y = cosh…

A:

Q: Determine the first derivative of the ff. function y = Vxe2* cos x

A: Derivative of a function gives the tangent of the curve at a given point. Derivatives are used to…

Q: find the first and second derivatives of f(x) = ln (x+1)

A: f'(x)=1x+1 and  f''(x)=-1(x+1)2

Q: Find the relative extrema using first derivative test   f(x)=(x-2)^6

A: Consider the function f(x)=(x-2)^6

Q: Compute the second derivative of f(x)=ex+x at x = 1 using a step size h = 0.2

A: To find the second derivative of f at x = 1. The approximation formula for second derivative at a…

Q: Find the instantaneous rate of change of g(x) = In(x + 3) at x =

A:

Q: dx V9-x2

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: 3. The derivative of f(x) = In x at x = 3 when h = 0.002

A: 3) To find the true error and relative error of the function: f(x)=ln x, x=3 & h=0.002

Q: Find the derivative of the logarithmic function. 3x f(x) = In %3D x+2,

A:

Q: Find the rate of change of f (x) = x° at x = 2. %3D

A: Rate of change.

Q: Shows that if a function f(x) is continuous in interval [a,b] then most likely the derivative of…

A:

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

A: Given function is

Q: What is the difference of antidifferentiation and anti-derivative?

A:

Q: 10. Find the first derivative: f(x) = (x³ + 2x) In x %3D

A:

Q: k(x) = x In x %3D

A:

Q: What is the instantaneous rate of change of the function f ( x ) = 5 /x  at x = 3 ?

A: Given,        The instantaneous rate of change of the function fx=5x at x=3.We know that,…

Q: How do you find the partial derivative of a given function using the definition formula?

A:

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

A:

Q: Find teh average rate f change of f(x)=3x^(2)-x from x_(1)=-1 to x_(2)=2

A: Solution: The objective is to find the average rate of change of the given function

Q: Find the derivative of -3x f(x) = e¯* + e2x - e %3D

A:

Q: nd derivative of f(x) = x In(x)

A: We have to find the second derivative of the given function

Q: compute the rate of Change of the functioN at x= a. flx)= -2X²-X,Q= -5 instantaneous

A: Given function: fx=-2x2-x

Q: Find the derivative of the function.

A: Given

Q: Determine the instantaneous rate of change of the function f(x) x4 at the point where x = -2.

A: instantaneous rate of change of a function is differentiation of function at that point

Q: (a) Show that the derivative solution of this function y = x** is x(x*+x-1) [1+x In x (In x + 1)] dx

A:

Q: Calculate the derivative of the function y=log2 x ln (2x) at x=1.

A:

Q: (4)The instantaneous rate of change of f(r) = e- at a = 1 is . .. (5) The derivative of f(x) = sec2…

A: (4) We have So we get the instantaneous rate of change of the function at  as .

Q: The function whose derivative is given by f'(x)=(x-¹), x 2. What is the #+2 critical point of f?

A: Critical point of a function is a point where either the derivative of function is zero or not…

Q: 1. Find the second derivative of y = sec-'x+ csc-!x. a. 0 b. C. +x+ d. -1 2. е.

A:

Q: Find the second derivative of y=x-1 at x=2

A:

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.