-у %3 (8ӕ — 6) sin (8z — 6)

Q: sin x Let g(x) = . 1 Find the derivative a'(x). dt . 2 1+t3 cos? x 1+ sin x sin x 1+ cos³x cos X 1+…

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Q: Equal derivatives Verify that the functions f(x) = sin? x and g(x) = -cos? x have the same…

A: fx=sin2x  &  gx=-cos2x Differentiating fx=sin2x with respect to x, we get…

Q: y =-(1-sin(x²)) 2 ||

A: Given:     To determine: Derivative of the given trigonometric function.     Concept: Chain rule of…

Q: Find the derivative of the function given below. k(a) = sin (a) cos"(a) k'(a) =

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Q: Find the derivative of the function. f(θ) = cos(θ2)

A: ven that , f(θ) = cos(θ2)Differentiate both side with respect to θf'(θ) = -Sin(θ2) .ddθ(θ2)⇒f'(θ)…

Q: Calculating derivatives Find the derivative of the followingfunctions.

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Q: d 1 11. (-) dx x A.

A: The given function is f(x) = 1/x f(x + h) = 1/(x + h)

Q: Second derivatives Find y′′ for the following functions. y=sec(x)csc(x)

A: Given,           y=secxcscx

Q: Calculating derivatives Find the derivative of the followingfunctions. y = tan x + cot x

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Q: 3 |cos = 3 find y' cOs У

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Q: DIFFERENTIATION OF INVERSE TRIGONOMETRIC FUNCTIONS 5.) y"'of y = x(sin Inx – cos Inx)

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Q: 1-x sinh Find the derivatives . 1+x

A: To find the derivative of:sinh-11-x1+x

Q: 5. y = Arctan² (x³) '2х-1 6. y = Arccos 3x+1/

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Q: Calculating derivatives Find the derivative of the followingfunctions.

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Q: INVERSE TRIGONOMETRIC FUNCTIONS: Find the first derivative of the  given function.

A: Since multiple questions are asked , I am answering the first question

Q: Composition of three functions Calculate the derivative of sin (cos x )2.

A: We have to find the derivative of function: sin cos x2 We know the formula of derivatives,…

Q: Question Find the derivative of f(x) = 2 cos x – 8x.

A: Given that, f(x)=2cosx-8x

Q: Derivatives of Inverse Trigonometric, Logarithmic, and Exponential Functions y= cos-1(sin x)

A: The function is y=cos-1sinx.   Differentiate the function with respect to x.…

Q: Sin 2x- Cos 2.x Sinh (u-v) = Sinh u.Cosh v - Cosh u.Sinh v %3D

A: See the attachment

Q: Derivatives involving ln x Find the following derivatives..

A: We have to find the derivative of function: dlnsin xdx We know the formula of derivatives,…

Q: Showing all steps show why the differential of Tan (x)is equal to sec? (x) (f) Question

A: Given problem:- Showing all steps show why the differential of Tan (x)is equal to sec²(x)

Q: DERIVATIVES Find the indicative derivative of the following: 1. y = V4x5 + 2x* – 5; y

A: The given function is y=4x5+2x4-5. The derivative of a function is found by differentiating the…

Q: DERIVATIVE OF TRIGONOMETRIC AND INVERSE TRIGONOMETRIC FUNCTIONS. Find dy/dx, '2x-1 1. y = Arccos…

A: To find: The derivative of y=cos-12x-13x+1. Formula used: Chain rule of derivative: fgx'=f'gx·g'x…

Q: Calculating derivatives Find the derivative of the followingfunctions. y = cos2 x

A: We have to find derivatives: y=cos2x We know the derivatives formula,…

Q: Calculating derivatives Find the derivative of the followingfunctions.

A: Given :          y=tan t1+sec t

Q: Va2 – x2 y = Arcsin-+ to

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Q: f (x) = sin (4x + 7x*)

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Q: Implicit and logarithmic differentiation Find the first derivative R(t)=[Sin(4t)]^6t

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Q: Derivatives of other trigonometric functions Verify the following derivative formulas using the…

A: The secant function in terms of cosine function can be written as sec x=1cos x. Tangent function can…

Q: Derivatives of bx Find the derivatives of the following functions.

A: Given : y = 4-xsinx

Q: Using the derivatives of trigonometric functions, the derivative of y= cos (z Aý = - sin (z) B. V --…

A: We have to find derivative

Q: Calculating derivatives Find the derivative of the followingfunctions.

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Q: 3. f(x) = (tanh(sin-1 x))2*

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Q: (x2+/x)cos(x) find the value of the first derivative at x= 2. sin(x) 12. Given the function f(x)=…

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Q: Calculating derivatives Find the derivative of the followingfunctions. y = ex(cos x + sin x)

A: Consider the given function, y=excosx+sinx use the product rule of the differentiation which states…

Q: z +1 Q (2) = tan- (z)

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Q: Derivative practice Find the indicated derivative for the following functions.

A: Our Aim is to find the derivative ∂z∂x for the function given below:-1x+1y+1z=1

Q: Find the 58th derivative of the function f(x)=cos(x). The answer is

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Q: Calculating derivatives Find the derivative of the followingfunctions. y = sin x cos x

A: given funnction, y=sin x cos xwe have to find derivative of given function

Q: 2. у%3D cos ? (2х — 1)

A: dy/dx = -2sin(4x-2)

Q: 5. y = Arctan²(x³) 2х-1 6. y = Arccos 3x+1/

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Q: -1 2. y = sec 6x2 – 3x + 2) |

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Q: Derivatives of Trigonometric Functions d (sin x) = cos x dx

A: Topic = Derivative

Q: Calculating derivatives Find the derivative of the followingfunctions.

A: to find the derivative we will use the quotient rule which says  here v = 1+cos x and u = 1-cos x…

Q: d (2х* Зх 3) dx

A: Using basic differentiation formulae: ddx2x2    3x     3=d2x2dx     d(3x)dx    d(3)dx

Q: Sin" (Зx - 4х*) Find the derivatives

A: we have to find the derivative of the following

Q: Implicit Differentiation. dy There is need to simplify. da Use implicit differentiation to find a.…

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Q: Derivatives Find the derivative of the following functions

A: Consider the provided function, y=23+sinx ...... (1) Find the derivative of the above functions.…

Q: d 7.- (2) dx

A: The differentiation of a constant term is zero. Whereas. if constant term is with variable then its…

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: