Answer: f'(x) = b. f(x) = In (x – + 15)

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A: The given function is fx=x3+cos x. Evaluate the first derivative of the given function as follows.…

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A: Given that, We have to find the value of  For that simply follow the step given as below

Q: Find the 1st derivative: Complete Solution.  y=2cos2 t/2

A: y=2cos2 t/2

Q: Find dy/dx by implicit differentiation   x2 + xy -y2 =4

A: Differentiate both sides with respect to x. For xy use product rule

Q: Find the anti-derivatives, using ONLY basic rules + 3* ) dx

A: Note:- We’ll answer the first question since we answer only one question at a time. Please submit a…

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

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

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A: Derivatives formula ddxcos-1x=-11-x2 ddxxn=n xn-1

Q: FIND ANTI DERIVATIVE a) S 2. +9 dx x マ d x 1-4x6

A:

Q: dy by implicit differentiation if dx 3 9. = 1. Find - -

A: The given function is 3y+9x=1

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A: Given:ln(0.9)

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A: We first separate the variables and then integrate  c= integrating constant Formula used:

Q: 2x2+x dx x+1

A: Integration ∫2x2+xx+1dx

Q: 10. S(2x – 3) dx e 2x2 - ебх

A:

Q: Find dy/dx by implicit differentiation. 5x + y = 8 + x²y²

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Find the relative extrema of f (x) = 7+ 144x – 9x? using both first %3D and second derivative tests.…

A:

Q: 5) Find the second derivative of f (x) = %3D ex plify your answer as much as possible

A: fx=1-2xexTo find the second derivative

Q: Find the derivative a) y = x sinh-(x) – Vx² + 1 b) y = cosh-(2Vx +1)

A: The derivative is calculated as:

Q: What is the derivative of * y = arctan(x2 + 1)?

A:

Q: 3x V1-x x = 0. y(x) = at Equation of the tangent line

A: Given,           yx=3x1-x2 at x=0

Q: A) Consider the function f(x) whose second derivative is f"(x)=4x+3sin(x). If f(0)=4 and f'(0)=4,…

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…

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A:

Q: Find dy/dx by implicit differentiation. x2 + xy - y2 = 4

A: Given function is, x2+xy-y2=4.   It is implicit differentiated as follows:…

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

A: Find your answer below

Q: B) Using the definition of derivative, find dy -if y = dx 1-x

A:

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

A:

Q: Find dy/dx by implicity differation.

A:

Q: 2. S- x²+1 dx x3+3x

A:

Q: The antiderivative of the function sin (Gx+7) is:

A: Given : sin12x+7

Q: 9. For f(x) = arctan (2 sin ( Vx )) , compute the first derivative at the point %3D X =

A:

Q: (a) By using the chain rule and the derivative = (xl) if x>0 (-1, if x< O' dx find - (Ix – x|)DvxE…

A: Given : ddx(x)=1 ,     if x&gt;0-1 , if x&lt;0 To find : ddx(x3-x) , where x∈(-1,1) and x≠0

Q: Q2: What is the value of second derivative of f(x)=3 sin((1-x)/t) *

A:

Q: What is the derivative of y = arctan(x² +1)?

A: Find the derivative of the function

Q: n. y= (x+Inx)

A:

Q: Find the derivative: f(x) = cos 1 + e8x 1- e6x – ebz f'(x) =

A:

Q: f(x) = x*Inx

A: TO FIND 5th order derivative f(x) = x4 lnx FORMULA USED  BIPART PRODUCT RULE OF DIFFERENTIATION…

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A: The derivative of a function gives the rate of change of a function when an infinitesimal change is…

Q: If f(x,y) is a real valued function of two variables then what is the second derivative of f?

A:

Q: Find the derivative dy/dx by implicit differenciation.  x2 + y2  = 100

A: Differentiate both side with respect to x and use the formula for differentiation formula for x^2…

Q: Find the particular antiderivative of the derivative f'(x) = 3 -+x that satisfies the condition f…

A: Follow the procedure given below.

Q: The derivative of y=eSinh/x +cosh¬/x equals

A:

Q: dy Find dx if y = V5- x2 , by using definition .)باستخدام صيغة تعريف المشتقة( formula of derivative

A:

Q: Find the linear approximation of f(x)=lnx at x=1and use it to estimate ln⁡(1.3) L(x)=? ln 1.3≈?

A: First find the linear equation at x=1  then find the approximate values

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A: Given fx=sinx at π4, h=0.01,0.2

Q: I FIND THE SECOND DERIVATIVE OF THE FF IN ITS SIMPLIFIED FORM х 1. y= Arctan- 3-V9-x²

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Find dy/dx by implicit differentiation. x4/3 + y4/3 = 1

A: Given that: x4/3+y4/3=1

Q: Find the derivative of the function y, below. y = 2x(ln x + In 7) – 2x + V2 dy da

A:

Q: Q Find the derivative us ing the de fini tion 2. O fcx) Fcx) x+2X %3D

A: Derivative of the function using definition

Q: Find the 1st and 2nd derivative of: Vx + Jy = va

A: