5. a) Find the first order derivative of the following function. y x° In x

Q: 5. Find the first and second derivatives of y if y is a function of r defined implicitly by x* + y*…

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Q: 2. Compute the derivative of the following functions: 1-e-* (a) f(x) = V1 – sin³ x, (b) f(x) =

A:

Q: y= In(In.x)

A: t differentiate wrt x

Q: Find the derivative of the function.

A:

Q: Solve for the 4th derivative of function K K= x3Cos√x

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Q: 6. Find the tangent line to the function f(x) = 2x cos"(x) (0, 1).

A: To find the slope we need…

Q: 1. Compute the derivative of y = tan2(42)

A: Answer and explanation is given below

Q: Q5:- Find the first order derivative of each of the following functions: a) y = esin-ix + In (cosx)

A: Given: y=esin-1x+ln(cos-1x) We know that ,  1. ddxex=ex 2. ddxlnx=1x 3. ddxsin-1x=11-x2 4.…

Q: Find the derivatives of the functions in Exercises s = cos^4 (1 - 2t)

A: The given function is s=cos4 1-2t. Obtain the derivative as follows.

Q: Q1:- Find the first order derivative of each of the following functions: b) y = tan(secx2)

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Q: 4. Determine the derivative of the function with respect to x. 8sin?(x² + 2) y = 4tan²(x² + 2)

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Q: 01:- Find the first order derivative of each of the following functions: (1+x)3 sec(x2) y = ex.sin2…

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Q: Find the derivative of y = ecos t

A: To find the derivative of y=ecost. Solution: Chain rule of differentiation states that:…

Q: 1. Find the derivative of the following function: f(x) : (x² sin- if x ± 0 if x = 0

A:

Q: Compute the derivative of the given function. g(t) = 2t - In(2 – 5t) %3D

A: Given that: g(t)=23t.ln(2-5t)

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 11) y = In 1-x (x +4)3

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Q: Find Find the second derivative of the given function. y = In(x² – 1)

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Q: 1. Compute the derivative of the following function: F(x) = [²dt sin

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Q: Y = c 2.

A: The product rule of differentiation is given by the following expression:- ddx(uv)=udvdx+vdudx The…

Q: Find the derivatives of the functions in Exercise . y = (1 + x2) e^tan-1 x

A: Given,          y=(1+x2) etan-1x

Q: 1. Compute the first, second, and third derivative of a. f(x) = x² In(x+ 1)

A:

Q: 1. Compute the derivative of the following function: F(x) = Jsin x

A: The function is  F(x)=∫sin xext2dt

Q: In(5æ) Find the derivative with respect to x of y = %3D 5x y' = | %3D

A: Find the derivative

Q: 4. Find the derivative of the following function 1 y = xtanx + -

A:

Q: 4) a) Determine the simplified expression for the 623rd derivative for the function f(x) =cos(2x)…

A: a)   fx=cos2x+sin2π     =cos2x+0      = cos2x

Q: Find the derivative of the function y = In(8 – e-a f'(x) =

A: We have to find derivative

Q: Q1:- Find the first order derivative of each of Inx a) y = e*secx + CsCx

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Q: Find the derivatives of the function defined as follows.

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Q: In (6x) Find the derivative of y with respect to x if y = sin (3e) dt.

A: the given function is: y=∫0ln(6x)sin3et dt we have to find the derivative of y with respect to x.…

Q: find the derivative of y with respect to the givenindependent variable.

A:

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

A: Given,

Q: Find the derivative of y with respect to x in the following functions: y= Ju +2u and u x2-3

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Q: (-- If y = then the derivative of y with respect to r is:

A: y=x-1x-1To find dydx

Q: Find the derivatives of the functions defined as . y = cos4 x

A: Given function, y = cos4 x

Q: Find the derivative of y with respect to s. (56° +3) У3 sec

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Q: find the derivative of y with respect to x, t, or θ, as appropriate.

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Q: Can you help me step by step?

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Q: 29. Prove the following derivatives by using the definition of derivative. (a) (") = n. dx nxn-1

A: topic - derivative and limits

Q: Find the derivative of y with respect to the independent variable. y%3D(In 60)

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Q: 3. If the derivatives of h with respect to U; for h=²u

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Q: Give the derivative formula for the function. (x)2 In x -e j'(x)

A: Consider the given function.

Q: 13 Find the secord derivative cy") y= x°+3x - when

A: see below the answer submit the q12 with what to do with the question

Q: 6.) Find the derivative of the fonction 2 8- g'cx) =

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Q: (3) Compute the derivative of the function Cos tdt.

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Q: 2. Find the derivative of h with respect to u if h = n²u

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Q: Monday, 1) Find the derivative of the given function with respects to e y = 3lan® In 3

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Q: 7. Find the second derivative of the following function: y = e** +In(7e¯* + 5x³) – 5²× +-

A:

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: