a) Find the derivative of the following functions: i) f(x) = x Inx ii) f(x) = iii) f(x) = 1 4* iv) f(x) = logs x %3D b) Find the derivative of each the following Trigonometric Functions. cos.x-1 (i) F(x)=. X 3 (ii)f (x) = 4sin³x + 4cos³x

Q: Find the derivative of the trigonometric function. У %3 бх сos(x) + x° sin(x) y' =

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: 1 FIND THE DERIVATIVE OF EACH FUNCT'ON. 1.) y= sin () a.) y= Tan( 3x) 3.) y= Cos( 3

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: When f(0)=0 and f(pi)=0, what is the derivative of the function  7e^x + 6sin(x), and what is the…

A: Let the given function be:Applying the derivative with respect to x:Derivative of ex is ex and the…

Q: Find the second order derivatives of the following functions Ax) (i)cos°x (i) sin x 3

A: To find the second order derivatives of the following functions. (i). Given function fx=cos3x. Power…

Q: -1 4. h(x) = x ( cos 2x ) at x = 0.1 5. f(x) = x Arcsec Vx at x = 2 %3D

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Q: 4. f(x) = x In x 5. g(x) = x tanx-In Vx2 +1 1+ sin x 6. y = In %3D 1+ sin x+ cos x

A:

Q: Differentiate implicitly the function y(x) given by the equation y=cos(x+y).

A:

Q: 5cos3(x) Гу 3 sin(3–2x) + tan? (3x? — 4х) — csc(/2x — 1

A: Differentiate y w.r.t x.

Q: 1 What is the lineur is The slope of the line tangent to the graph y = cos x at the point x =…

A:

Q: 13 Find the derivative of the function. Y = 2² + cos" (xx) a

A: Solution:- Given function is  y= a4+cos4(x)           ----------(1) Here, the variable is 'x' and…

Q: 1 3.| y = xSin(x) + (1 – ÷x²) Cos(x) (1-**) Cos(x)

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Q: (b) Find the first 4 derivatives of f (x) =b cos (x), and use the results to find the following…

A: We find the first 4 derivatives.

Q: Find the derivatives of the functions  1. y = x2 cot 5x    2. y = x-2 sin 2(x 3)

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: 1. Find the derivative of the following trigonometric functions a) y = x sin(x) + cos(x) b) y =…

A: Given the trigonometric function

Q: B) Find all of the second derivatives for f(x, y) = (3xy2 + 2xy + x²) In; x²+y² itable graph and…

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Q: 6. Find the derivatives of each function. a)f(x) = 3x4 – 4x² – 250 %3D b) g(x) = x/2 – x-1/2 %3D sin…

A:

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

A: Differentiation of the given function can be done with the help of differentiation formulas.…

Q: Find the second order derivatives of the following functions Ax) (i)cos³x (i)sin x 3.

A:

Q: COS 2. %3COS

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Q: (a) From sin2 x + cos2 x = 1, we have f(x) + g(x) = 1. Take the derivative of both sides of this…

A: (a) From sin2 x + cos2 x = 1, we have f(x) + g(x) = 1. Take the derivative of both sides of this…

Q: Find the derivative of the inverse trig functions. a) y = cos-1 5x b) y = x· arctan x

A: We can solve both the question as below.

Q: Suppose u and v are differentiable functions of x. Use the given values of the functions and their…

A: As we know that the derivative of uv form is given by ddxuv=u'v-uv'v2 see below the answer and…

Q: Find the derivatives of the functions r = 2θ√cos θ

A: Given: r=2 θ cosθ To determine: drdθ

Q: 13. We know that x = r cos 0 and y = r sin 0, then find the derivative af /ðr if f = x2 + y2

A: Given: f=1x2+y2, x=rcosθ, y=rsinθ For finding derivative of given expression with respect to r,…

Q: -1 Find the derivative of the function: y=6 sin ¹¹ (x²). y'= y'= O y'= 12x y'= -X 2x 2 + X 12x 4 4 X…

A: Given y =6 sin-1 (x2 )

Q: 1. Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A: Part 1 : Slope of tangent at (π2, π4) is given by dydx(π2, π4) ⇒y·sin 8x=x·cos 2x⇒ddx(y·sin…

Q: 1. a) Find the derivative of the function y = sinx + cosx. %3D b) What is the value of the…

A:

Q: Find y' by implicit differentiation. cos(x) + √y = 2 y' =

A: Explanation and solution is given below....

Q: (a) Find the derivative of the function g(x) = sin2 x + cos2 x (b) then use a trigonometric…

A:

Q: Find the derivatives of the functions

A:

Q: Find the derivative of y = cos³*+8 (x). Provide your answer below: y =

A: Given query is to find the series of the expression.

Q: 1) Determine the derivative o a) f(x) = -4e*² b) y = cos(3*) c) g(x) = -2 sin3 (2x) %3D %3D

A: Note: Multiple subparts are given, we are answered with first three parts only, if you need more…

Q: Solve for the derivative of the given functions using the Chain Rule formula. a.) Let f(x) = √(x2 +…

A: Solution

Q: Find the derivatives of the functions r = sin (θ2) cos (2θ)

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Q: f(x) = 2 cos I - 3:

A: Of a function y = f(x) of a variable x is a measure of the rate at which the value y of the function…

Q: (a) Find the derivative of cos(1+x²).

A:

Q: b) Use implicit differentiation to find for the equation yz? -e** cos (4zx)–3y² =4. F. DO NOT use…

A:

Q: (A) Find the first derivative of the following function: 1+ cos2x f(x) = %3D 1- cos2x |

A:

Q: Find the derivative of the following: 1. y = 14 tan x cos x + 10 csc x 2. g(x) = sin?x + cos²x + sec…

A:

Q: The derivative of y = 3 cos (V1-x²) + (1-x²) ² can be written as 3 1– x² sin ( V1-x²) - (1-x² ) 7 3x…

A:

Q: 7. Find the second derivative given g(x) = sin x² A. 2(cos x? – x sin x?) B. 2(cos x? – 2x² sin x²)…

A:

Q: The derivative of the function f is defined by f'(x) = x? – 5x + 5 cos (3x? – 3x). If ƒ(-2) = –4,…

A: Given: f'x = gx = x2-5x+5cos3x2-3xf-2 = 4------------------------------Aim: To find absolute maximum…

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

A: Given, y=-cos2x+cosπ6

Q: Find the first and second derivatives of the function. f (x) = In(cos x)

A: We will use the chain rule and quotient rule of differentiation to find the first derivative and the…

Q: 3:B/ Identify each function and find derivative of y with respect to x a) y = x tanx 1+secx b) y =…

A:

Q: 1. If f(x) = cos²x, then the derivative, f'(x) = ? a) 2sinx b) −2 sin x cosx c) 2cosx d) 2 cosx =…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: 1. Find the derivatives of each function then simplify completely. f (x) = 2a - 5a2-+5 y = x'V? +3…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: I Find the second derivative (y") of the following functions and simplify the final results. 2sin…

A: topic - double derivative of a function

Q: Suppose u and v are differentiable functions of x. Use the given values of the functions and their…

A: Given:

Q: Find the first and second derivatives of the function  y = cos (x 2 )

A: We have to find first and second derivatives of the function: y=cos x2 We know formula of…