1. h(x) = 5f(x) – 4g(x) Answer. h'(-2) =

Q: y = In (x* + 5)³

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Q: 1. Find derivative of given function defined as follows. y = (8x²-3x³) ³

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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: 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: Find the first derivative of the following functions Y = x5 e-3 ln x and Y = ln √ [ (x – 1 ) / ( x…

A: Solution is given below:

Q: What is the derivative of 1+x3 at the point (1, )? O 1/4 O- 1/4 O 1

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

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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: when in a derivative problem is e^( ) =0 and when is not?

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Q: 2.) Find 1st derivative of y = e-'In (x-1)

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Q: The 2nd derivative of the given functions is 3 ponts y = 3 cos (4x- 5) None of the above -48 cos…

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Q: 1. Explain two different ways to solve for the derivative of s(0) = 200sin cose

A: The given function is : s(θ)=200sinθcosθ We need to find the derivative in two ways.

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

A: As we know that: The product rule: f·g'=f'·g+f·g' The chain rule: fgx'=f'gx·g'x The Power law:…

Q: Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the…

A: Use the basic definition of Cosh to find the derivative of the function, Coshx=ex+e-x2. Find the…

Q: 4. If y = x cos x determine the 5th derivative. [y(5) = (60x – x³) sin x+ (15x² – 60) cos .x]

A: To find out the fifth derivative.

Q: 2х Find the second orfer derivatives of y=Tan" 1-x3

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Q: 2. Find the derivative of y= ecos{/x+3) Solution:

A: Topic:- derivatives Note:- as per our guideline if more than one question uploaded than only first…

Q: y = e* (In x)² %3D

A: Here we want to find the first derivative of the given function. For finding the derivative we use…

Q: 15 - What is the approximate derivative of f(x) = 5x° + 4x? if we use forward difference method,…

A: Derivative of function at any point gives the slope of tangent to the function at that point.…

Q: 4. Find the second derivative of Y with respect to x for 4x² + 8y² = 36

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Q: 1 Find the function whose derivative is (x+1)-

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Q: In(x), Sn (4t + et) dt. Find the derivative of F(x). 3.

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Q: 1 14) Use the definition of derivative to find dx 3- х.

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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: Example 2: by using the definition of the derivative, find dy/dx of the function y = 5x + 8x - 3x +4

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Q: 6 Find the 3rd derivative of y = (x-1)2

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: Suppose that the first derivative of y = ƒ(x) is y' = 6(x + 1)(x - 2)2. At what points, if any, does…

A: Given the first derivative is: y'=6x+1x-22

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: Suppose x and y are variable (y is a function of x) that satisfy the equation Sin(x+y)=xy, What is…

A: To find the derivative of y with respect to x

Q: Suppose that the first derivative of y = ƒ(x) is y'= 6x(x + 1)(x - 2). At what points, if any, does…

A: The derivative of the function y=f(x) is y'=6xx+1x-2. We have to find at what points, if any, does…

Q: 22 Find the 43rd derivative of (1 + x²)“ at x = 0. 0.

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Q: 1. 8rd Derivative of fC x) = 4 x³ - 8x5 1

A: We will use just the basic knowledge of differential calculus to answer this question step-wise.

Q: 4. Find the first derivative of y = 170x tan (20x)+- In(49 – x 5e7-8cos

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Q: Example 2: by using the definition of the derivative, find dy/dx of the function y 5x' + 8x - 3x +4

A: We can use definition of limit In order to solve the given problem.

Q: Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the…

A: Given: y=sinh(3x2 ln(1+3x)) Use chain rule for derivative: ddx(f(g(x))=f'(x)ddxg(x) And uv rule for…

Q: Two equivalent forms of the Chain Rule for calculating the derivative of y = ƒ(g(x)) are presented…

A: Two equivalent forms of the Chain Rule for calculating the derivative of y = ƒ(g(x)) are presented…

Q: What is the second derivative of f(x)=−x4? at the point x=−3 Do not include "f′′(x)=" in your…

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Q: 5. Find the first derivative of y = (2x³ – 1)5 Vx² – 1

A: Given: y = (2x3 – 1)5√(x2 – 1)

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

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Q: The graph of a particular function passes through the point (3,4). Its first derivative is 2yy' + 2x…

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Q: x3+6x-2 dx x4+6x2

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Q: Find the differential of the function y=lntan2x at x=π/8.

A: Given: ,at x=π/8 Differentials are infinitely small quantities. Use the term for differentials as…

Q: 16. What is the derivative of the function: * y = sin(6x² - 1) y = 12x cos(6x² - 1) y' = x cos(6x² -…

A: Solving the problem by finding the value of the derivative.

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: Suppose we are asked to compute the 100th derivative of x 3 . How can we obtain the answer in a fast…

A: Solve the following

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

A: The given function x2+3xy+y3=10

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

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Q: 4. If y = x cos x determine the 5th derivative. [y6) = (60x – x³) sin x+ (15x? – 60) cos x] |

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Q: Suppose that the second derivative of the function y = ƒ(x) is y'' = x2(x - 2)3(x + 3). For what…

A: Given that, y=f(x) Second Derivative is y'' = x2(x - 2)3(x + 3). As we know that, Inflection point…

Q: 4. Find the 2nd derivative of f (x) = 4-x x)%3)

A: To determine the second derivative of the function given by; f(x)=4-x Differentiate the function…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.