Find the natural domain and the derivative of the given function. (a) ln(4x + 2) (b) x · cos x (c) sin(3x2 + 5)

Q: 3. Use logarithmic differentiation to find the derivative of y with respect to the given independent…

A: we have to find the derivative of y by using logarithm.

Q: Find the derivative of the function. f(x) = ln(5+e^x/5-e^x)

A: Use derivative formula :- f(x) = lnx then derivative f'(x) =1/x

Q: 5. Find the derivative of: a. f(x) = cos(e³x-4)

A:

Q: Find the derivative of the function.

A:

Q: 1. Find the second derivative of the function. 8(x) = 3\/x + e7*In(x)

A:

Q: x-2 Find the 1st derivative of y= sin x+3

A: To find the first derivative of y=sinx-2x+3. Solution: Chain rule of differentiation states that:…

Q: Find the first derivative of g(x) = - 9e* tan(x). : (x),6

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: 2х- 3 3. У3 5x +1

A:

Q: ln(x+(x2 −16)^(1/2)) Find the domain and the derivative of the function.

A: Given, function is

Q: y = In- e 2x+1

A:

Q: Find the derivative of the function. f(x) = ln   x + 2 x − 2

A: Given,            fx=lnx+2x-2

Q: Can you help me with this problem step by step?

A: The equation is given by

Q: 1 Find the derivative of g(x)= (x)sec(x) + a+ x* + cos - sin(x)

A:

Q: COS 2. %3COS

A:

Q: Find the second derivative of the function. 3root(x) + e^(6x)ln(x)

A:

Q: Find the derivative of the function. g(x) = ln(8x + 3) g(x)=

A: We have to find the derivative of the function.g(x) = ln(8x + 3) Here we will use the formula of…

Q: 6. Find the derivative of f(x) = x² – 3x. Use the result to find the slope of the tangent line to…

A: By using differentiation. and definition of tangent at point.

Q: 4. Find an equation of the tangent line to the graph of f(x) = ln(x ^2 + 4) at the point (2, ln(8))

A:

Q: Determine whether the following statement is true or false, and explain why. The derivative of ln kx…

A: if y = ln x Then y'=1x

Q: cos (5x-0.1) w(x) =- e*

A:

Q: find the derivative of ln(3x^2+e^x)

A:

Q: 10)Find the first derivative or f’(x) of the following functions using long method derivatives

A: We need to find derivative of given function.

Q: Find the derivative of y with respect to x. y = csc-1(x5 + 1) ; x > 0

A:

Q: Find the derivative of the function. f(x) = ln(x2 + 1)2

A:

Q: g(x) = cos ¹x+ 1-x

A:

Q: 4 a. Use implicit differentiation to find the derivative dy/dx of the given function. b. Find the…

A: The objective is to find the derivative and slope at the point .

Q: ) .3 Find the derivative of h(x) = cos (2x – 5 %3D

A: Given,            hx=cos42x3-5To find : The derivative of the given function.

Q: Find the derivative of the function. h(x) = ln[(−6x + 3)(x + 3)]

A:

Q: a) Find the derivative of y = 2 sin-1 x. b) What is the value of the derivative at x = 0.

A: given

Q: (a) Find the derivative at x = −1. (b) Find the second derivative at x = −1.   h(x) = 2x4 + 8x3 +…

A: (a) The given function is

Q: 17) Find the derivative of y = x? COs x - 2

A:

Q: 3x-4 1. Y= Arctan 4

A:

Q: Find the derivative of the function. f(x) = ln(8x + 9)

A: Given, f(x) = ln(8x + 9)  We have to find the derivative of the function.

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

A:

Q: f(x) = sin (x³)

A:

Q: 1. Use logarithmic differentiation to find the derivative of the function. y = x4 cos(x) 2. Use…

A: Here we have to find the derivative of the given functions using logarithmic differenciation.

Q: x' Find the derivative of h(x) sin x 4x2+2

A:

Q: 32. Using one-sided derivatives, show that the function f(4) = { 3x, x>1 does not have a derivative…

A: Given: fx=x3,   x≤13x,   x>1 To Find: To show that the given function does not have a derivative…

Q: 2 a) FIND BY IMPLICIT DIFFERENTIATION: x*y³ = -8 %3D dx b) EVALUATE THE DERIVATIVE FROM PART a AT…

A: Given: x4y3=-8

Q: 3. Find the derivative of (a) f(x) = (x + 2 sin x) (1 – 6 cos x), and (b) g(x) = sin x/ 7x

A:

Q: (x²+1)* Find the derivative with respect to x: y = In /1-x

A: The given function is: y=lnx2+151-x

Q: 1+sin 2x 1) Find the derivative of f(x) = 2 cos x

A: To find The derivative of given f(x)

Q: Find the derivative of the function h(x)= ln(5x+1/7x-2)

A:

Q: Find the derivative of a. (e(sin2x))/[In(cos2x)]2

A: We have to find out derivative

Q: 1) Find the derivative of the function: (3х — 1)3 Vx* — 1 f(x) = cos² x

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the first derivative of the function y = In[tan (pi/4 + x/2)

A:

Q: what’s the derivative ? f(x)= ln(x^3 - 7x^2 + 1)

A: topic - derivative of a function

Q: What is the derivative of the function h(x) = ((4x^2-4)/(cos(x)))^8

A: We have to find the derivative of ((4x^2-4)/(cos(x)))^8 = 4^8(x^2-1) sec^8(x)= 65536(x^2-1)sec^8(x)

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: