11 In(x)sin (x²). Find the first derivative of g(x) (x),6

Q: Determine the first derivative of the ff. function y = tan(ln(cot(x² + 3 ln 3x)))

A: Chain rule of differentiation: f(g(x))'=f'(g(x))g'(x) Formulae used: ddxtanx=sec2xddxlnx =1xddxcot…

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

A: Given Data: Function: fx=x3+2xlnx The product rule of derivative is, ddxfx·gx=fxddxgx+gxddxfx Use…

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

A:

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: Find the first derivative of y = e3x. 3e3x

A:

Q: Shows the derivative function of: 2x² + ln x²(2x² + 5x − 1)

A:

Q: The derivative of y = 2 ln ⁡ x − ln ⁡ x 3 is

A: The given function is, y=2lnx-lnx3

Q: 17) Find the first derivative of f(x) = (cos4x)6 6 or f(x) = cos 4x

A:

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

A:

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

A: Given the  y = ( ln x)^4 We need to find the first derivative . Therefore differentiate to given…

Q: Compute the derivative of f(x) = 7 ln (x + 10) + In (x³ ): Answer: f'(x) =

A: Given function is  f(x)= 7ln(x+10) + ln(x3), we have to find the derivative of f(x) with respect to…

Q: y = ln 1-x² 1+x²

A:

Q: 2х- 3 3. У3 5x +1

A:

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

A:

Q: Find the first and second derivative of any function defined implicitly by yx2+ y2= x

A: Given,           yx2+y2=x

Q: In the given question as follows, find the derivative of the function.   y = ln(2 - e5x)

A:

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

A:

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

A:

Q: 18) Find the first derivative of y = 1 -sin² x - 4

A: The given function is: y=14sin2x

Q: 8. Find the derivative of the function. y= In(1+x)

A:

Q: Find the derivative: y = 6 In x 6 ln x-1 x7 1-6 ln x 12 1+6 ln x x12 4 O 1-6 ln x x7 O

A:

Q: Find the derivative. [미 In dx x +3 x-3

A:

Q: 26 Find the 155th derivative of (1 + x°)" at x = 0.

A: see 2nd step.

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 derivative of ln(3x^2+e^x)

A:

Q: 3) Find the first derivative of y=(In x)"

A: According to our guideline 3 subparts of question or the first question can be answered and rest of…

Q: Find the derivative of y= ln (6X^2+3X)^3/(7X-2)

A: Topic-Derivative

Q: Find the derivative of the following function. y= 4 ln x – In(x-8)

A: we have to derivative

Q: Find the derivative of the function. y = x2 ln x2

A: Consider the provided question, We have to find the derivative of the given function,

Q: Find the derivative of the function. Y= q56* In(2)ln(5)ln(6)· 3*. 5".; 2:56*+1+x

A: Given problem:-

Q: Find the first derivative of = (ln x)* 4 y

A: From the given function; y=lnx4 We know that; The Power law: ddxxn=nxn-1 The chain rule:…

Q: 3// By using logarithmic differentiation and with respect to independent variable x, find the…

A:

Q: Find the second derivative of x² y² + xe = 2 sin y

A: Solution is given below:

Q: In(3x) Find the derivative with respect to x of y 3x

A: We will use the quotient rule of differentiation to find the derivative of y. Chain rule of…

Q: 5. Find the first order derivative with respect to y of the function U = In/x² + y² + z²

A:

Q: Determine the first derivative of the ff. function y = 400(2)*+3 sin 3x

A: Given: y=4002x+3 sin 3x To Find: First derivative of the given function

Q: Find the derivative of the function. f(x) = ln(x2 + 3)

A:

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

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

A:

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

A:

Q: (x² +SJ° In 14-X つ. dr

A:

Q: Find the first derivative of:   f(x) = ln [(5x+2)1/2 / csc(x)]

A:

Q: Find the first derivative of x² + 3xy + y3 = 10 implicitly.

A: The given function x2+3xy+y3=10

Q: 11) Find the first derivative of y = (ln x)*

A: We have to find the first derivative of given function.

Q: Find the derivative of the function y = 1/ln(1 − 7x)

A:

Q: Find the derivative of f(x)= ln x^2/x^2+1

A:

Q: Example 2.35: Using Implicit Differentiation to Find a Second Derivative d'y dx Find if x +y² = 25.

A: Explanation of the answer is as follows