Find (f-1)'(a). f(x) = x - , x < 0, a = 1 х (F-1y(a) = ||

Q: 13. f (x) = sinx3 (2х-1)2

A: I have stated the used formulas in the solution

Q: Find the first and second derivatives of the function. f(x) = In(x + 4) f'(x) = f"(x) I3D

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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 arctan(x² + 1) -2x O f' (x) = -2a2 – a4 2x f' (æ) = x² +2 2x f' (x) x4+2x²+2…

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Q: 2. (a) Find the derivative of f(x) = 2x2 – 2x + 2 from first principle sin x (b) If y = x + find x4…

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Q: 8. Find the derivative of f (x) = 2tanx – 3secx. Show all steps -

A: We have to find the derivative of the function fx=2tanx-3secx Then,…

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

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Q: Find the relative extrema of f(x) = 8+ 126x – 7x2 using both first and second derivative tests. f…

A: If second derivative is less than zero then there is relative maxima.

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

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

Q: compute the derivative f (x) = ln(4x2 + 1)

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: 1. Find the first derivative by using the definition for f(x) = 3x² – 2x – 5, hence - find f'(-2)

A: Derivative of a function is ratio of difference in output and difference in input.

Q: Find the derivative of f(x) = 2(x² + 3x) cos(sin(x³)).

A: I have used product re and derived of composition of two function

Q: 10. f(x) = cos (2x)e*²-1

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Q: What is the first derivative of q(x)= ln((7x^2+3x+7)/((x^5/6)(tan(x)))

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Q: How to find the critical points of this derivative

A: We have to find critical point of f(x),where f'(x) is given by:

Q: Find the derivative of ln(2x2)+ln(2x)+1/3 where x=1

A: Given,           The derivative of  ln2x2+ln2x+13 where x=1

Q: (b) Use implicit differentiation by partial derivative to solve for of function 3x2 + 2xy = -4y3. dx

A:

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: 9 Derivative of fi») 1x 4 . 5. 1 f) 1x1cosx, fird f'n)

A:

Q: Find sixth order derivative of the function f(x)=(x-5)^7.cos(5x) by using Leibnitz theorem.

A: n! = n × (n-1) × (n-2) × (n-3) × (n-4) × ............ × 1

Q: Use the sign of the derivative to establish the inequaltiy ln(1 + x) > x − x2 2 , ∀x >0

A: SOLUTION-

Q: find derivative of the U function 1-x f(x) = sec-1. 1+ x ーオ

A: Explanation of the answer is as follows

Q: 3. Find the derivative of f (x) tan (5x + 7), by first principle of differentiation

A: Given function is By first principle of differentiation, we have

Q: sinx 3. f(x)=(x)*

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Q: Example 4:- By using the four steps rule, find the derivative of the function f(x) = Vx + 2

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Q: 1) Find the second derivative of f(x)= 24\x . (6) 2) If y = cos x, what is y (x)?

A: To find the derivatives of the given functions.

Q: a the derivative of h(x) = ln + 2 x5 et |

A:

Q: Approximate the derivative of f(x) = x² + 4x + 5 at x = 3 using the forward, backward, and central…

A: f(x) = x2 + 4x + 5 h = Δx = 2 xi = 3         f(xi) = 26 xi+1 = 5          f(xi+1) = 50 xi-1 = 1…

Q: What is the approximate derivative of f(x) = x2e* , using backward-difference approach at %3D x-2…

A: The main objective is to calculate the value of the derivative of the function f(x)=x2ex at the…

Q: 2. Use central difference approximations to estimate the first and second derivatives of y = e* at x…

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Q: 3. Find the derivative of f(x). (a) f(x) = e cos x (b) f(x) = (2x³ 4x-¹) cotx -

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Q: Using the Chain Rule, compute the first derivative of sin 1–x.

A: chain rule Let f(x) = g(h(x)) And let u = h(x) Using the above, function f may be written as: f(x) =…

Q: Find the relative extrema of f(x) = 4+70x – 5x² using both first and second derivative tests. f (x)…

A: Given:- f(x) =4+70x-5x2  To find:- Relative extrema of f(x) using both first and second derivative…

Q: Find the linear approximation of the function f (x,y) = ln (x - 3y) at point (7,2).

A: To find the linear approximation of the function fx, y=lnx-3y at the point 7, 2.

Q: Find the relative extremum of g(x) = x - 3x +1 by using first derivative test.

A: Let g(x)= x3-3x2+1 To find the relative extremum , here we use first derivative test In this method…

Q: he first derivative of f(x) = ln(5X4 - 6x) will be

A:

Q: 2) Find the derivative of f (x) = tan(1 + cos 3 x) 3) Find the derivative of f(x) = Vx3 – 4x2

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Q: Q1: Calculate the 5th derivative of f(x)= (2x-5) sin x *

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Q: Solve for the derivative of the Inverse Hyperbolic Differentiation. 1. y = sin h-1 (2x2 - 1) 2. y…

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

A: Given f(x) = x2e2x

Q: Find the derivative of the function 3- y = e- sin 3x 4- y csc- (x2 + 1)

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Q: Find a function with the given derivative whose graph passes through point P f'(x)=1/x+2, x is…

A: The derivative is given as

Q: Using the đết of derivative, fin rivative of f(x) = x² + 2x + 2.

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Q: 9) Find the value of the derivative at the point x=2 if f (x) = xv2x – 7

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

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Q: 2. Determine the 8th derivative of y with respect to x of the function f(x) = 1 + x2 and find the…

A: fx=11+x2 Differentiate the above function with respect to x. f'x=ddx11+x2=2x1+x22 Again,…

Q: 8) Find the first derivative of f (x) = sin 2 (x3).

A: