Take the first derivative for each of the following functions: a) f(x)= cos3x b) f(x)= (e2x+3)(x2-1) c) f(x) = (3x+2)/(x2-5)

Q: 3x+4 3. f(x) = x2+3

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Q: Find the derivative of the following. Ax) = (x)sin x h(x) 1+ csc x 1- csc x

A: Given : f(x)=(x)sinx h(x)=(1+cscx)/(1-cscx)

Q: Consider the function f(x)  whose second derivative is f"(x) = 10x+4sin(x) . If f(0)=2  and f'(0)=3…

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Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

A: By the fundamental theorem of calculus if we have F(x)=∫f(x)dx then F'(x)=f(x). In some cases an…

Q: 2. Use rules of differentiation to find the derivative of the function 5a° (x- +3) g(x) = x2 +1 Show…

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Q: Find the derivatives of the function f(x) from the first principle  sin2x

A: Answer and explanation is given below...

Q: What is the first derivative of g(x) = In 4x²+4x+8 ? x 3 tan x

A: we use Logarithmic properties

Q: 1. f(x)= Vx3 + 2x² + 3 2. f(x) = (6x – 7)(2x + 3)

A: To find the second derivatives of the given functions.

Q: 3. Find the derivative of f (x) = 2x²e² tan x.

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Q: the derivative of a function f is given by f'(x)=((x^4)-1)/x^2. if f(1)=2, what is the value of…

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Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

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Q: Consider the function f(x) whose second derivative is f''(x)=5x+3sin(x) If f(0)=2 and f'(0)=3 what…

A: Given : f''x = 5x + 3sinx

Q: Give the complete solution Find the derivative of f(x) = 5x6 - sec-1(x2)

A: Complete solution is given.

Q: 4x +2 x-12 7. f(x) = 2x

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Q: Find the derivative of the function f(x) = {x3 - tan tan (4x2 -2)}4

A: The question is taken from the calculus in which we have to find the derivative of given function We…

Q: (1+x²-1) y = tan²¹ / √₁+x²

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Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

A: Given, f'(x)= sec22x; π2, 0

Q: 12 x+6x?+3x 5. f(x) = 3x Vズ-3 6. f(x) = ズー9

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Q: y = csch /sec(x³ + 2)

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Q: (f°9)(x) if f(x)=2x3 +1 and g(x)=6x +5

A: We have to find the composition of the function then have to find the second order derivative.

Q: Find the derivative using the first principle  F(x)= (x-1)(x-2)

A: Given F(x)=(x-1)(x-2) To find the derivative using the first principle From the first principle, we…

Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

A: The derivative is f'x=-sinx2   Integrate the function with respect to x.…

Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

A: Given: f'(x)=-2x8-x2,    2,7 Integrate the given function to obtain the function f(x). The formula…

Q: Find the second derivative of the function f(x) = sin (2x4)

A: This question is related to differentiation, We will solve it using given information.

Q: Let f(x)=9−(4x^2+3x). Then according to the definition of derivative

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Q: Consider the function f(x) whose second derivative is f''(x)=8x+10sin(x). If f(0)=3 and f'(0)=2 what…

A: The function is f"x=8x+10sinx.   Integrate the function.…

Q: Compute for the derivative of the function f(x)= Arctan (csc2 (3x2/3))

A: Some derivative formulas: ddxtan-1x=11+x2 ddxcscx=-cotx cscx Chain rule of derivative:…

Q: Find the derivative of f(x) = log, (3x4 − 2x²) at the point x = 3. Enter an exact answer. Provide…

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Q: Find the derivative of f(x) = arctan x In(6x? + 6x – 4) - 12x 1 1 In(arctan(x)) + In(6x² + 6x – 4)-…

A: The given function is fx=arctanxln6x2+6x-4

Q: 6 (x+2)(x-5)(x²+7) V(x3-8)(x+3)(x+4) %3D

A: Using Logarithmic Differentiation.

Q: Choose the correct value of derivative. d dx x+1 X () is equal to (Hint: Look at the note of section…

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Q: 1. f(x)= Vx3 + 2x² + 3

A: topic - second order derivatives

Q: Consider the function f(x) whose second derivative is f''(x)=2x+3sin(x). If f(0)=2 and f'(0)=4, what…

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Q: Find the derivative of f(x) = (5x 2 + 3x + 1) × (3x 2 + 2x − 1) × (x 2 − 1). Show all steps.

A: Given:f(x)=5x2+3x+13x2+2x-1x2-1

Q: Find the Do not include "f'(x) =" in your answer. derivative of f(x) = (-x³ - 2x² - 2x) sin (x).

A: Given f(x)=(-x3-2x2-2x)sin(x)

Q: f(x) = 3 sin 1 (x²)

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Q: Find the derivative of the following function by definition (from first principle): 1-x f(x) =. 2x

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Q: Find derivative of: g(x) = sin(x-3x2)

A: Given query is to find the derivative of g(x).

Q: f(x) = (6x – 7)(2x + 3) %3D

A: Given  f(x)=(6x-7)(2x+3)

Q: Find the derivative. Simplify completely. 1. f(x) = 4x³ cos x 2. g(x): Sx-4 In x 3. у sin x 4. f(x)…

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Q: find the derivative of the given function. f(x)= 3x2- sin(x)/x

A: Given

Q: Find the derivative of f(x) = log(-6x* – 6x + 5) at the point x = 2. Provide your answer below:…

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Q: Find the derivative of f(x)= 11x^2 at x=1 please use definition of derivative formula

A: Given :   y = 11x2    at x =1

Q: What is the derivative of f( x = zi; = x 3 ? Or(-) = 3 F(=) f'( x Of(2) = 3= F(=) OF(2) = }ei OF(-)…

A: To find the derivative of f(x)=x2/3

Q: Solve for the derivative of the function using chain rule. 6. f(x)= cot(6x3+5)

A: Derivative

Q: flx)= -e, 1-x2 1-e

A: To find The derivative of f(x).

Q: Consider the function f(x) whose second derivative is f''(x)=2x+7sin(x). If f(0)=3 and f'(0)=3, what…

A: to find f'(x) integrate the given function c=integrating constant. Then plug x=0 and f'(0)=3 and…

Q: f(x)=4 sin¹+x+√4x²

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Q: 1. 1. f(x) = 4x³ · cos x

A: Given: fx=4x3.cosx