Determine the domain of the function f(x) = V 3x + 5 sin(5x).

Q: What is the derivative of f(x) = 26 (12.1)* + 8 (0.56)* +1 ex with respect to x? f '(x) =

A: topic  -  derivative of exponential function

Q: Find the f( 6)(x) of f(4)(x)= (x2+1)2 Differentiation

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Q: Consider the function f(x) whose second derivative is f''(x) = 3x +4 sin(a %3D If f(0) = 3 and f'(0)…

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Q: Find y" by implicit differentiation. x² + 5y2 = 5 %3D

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Q: What is the derivative of f(x) = x² +x² a +2 where a is a constant ? xa+2

A: We write f(x) using exponents f(x)=x7+x2+a+2xa+2f(x)=x7+x2+(a+2)x-(a+2)

Q: B) Findfor the Implicit function: dx x² - sin(xy) + y² = 5xy

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Q: Find the derivative of the function f(x) = V(a3 + 7x) by using the definition %3D of the derivative.

A: Let's find.

Q: What is the first derivative with respect to x of f(x) = (x² – 4) (3x – 2)? a. (2x)(3) b. 6х (x + 2)…

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Q: Consider the function f(r) whose second derivative is f(z)- 8z+10 sin(r). If/@)- 4 and f'0)-4, what…

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Q: Find the second derivative [ f"(x)] of the given function: f(x) = eln Vx²+2 %3D (x2 + 2)) x(x² + 2)-…

A: Given problem:- Find the second derivative [f''(x)] of the given function:   f(x) = eln√(x^2+2)

Q: Find f(x), the most general antiderivative of the function: f" (x) = 18x – 3 sin(x)

A: Explanation of the answer is as follows

Q: 1 dx = +C (x+1)² X+1

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Q: Find the derivative of the function f(x) = 4v3x² – x. 12х - 2 A. V3x2-1 6х - 2 бх — 1 C. V3x2 –1 E.…

A: To find the derivative of f(x)=43x2-x

Q: Find the third derivative of ƒ (z) = ¥9z +I. f" (2) =

A: Answer is mentioned below

Q: Evaluate the function: dx (x+1)–Vx+1

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

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Q: Use the second derivative test to find the local extrema for the function f(x,y) = x² +y³ + 2xy – 3x…

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Q: Find the derivative using the definition. a. f(t) 2t+1 b. g(x) = 2x² +1

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Q: Find an analystic function whose real part is e-x (x sin y-y cos y)

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Q: Find the second derivative. 1 h(x) = x2 %3D | h"(x) = %3D

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Q: Find the derivative of the function. f(x): f(x) = 2xarccos(x) – 2/1 – x² 2arccos(x) + 2 2arc cos (x)…

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Q: B) Find for the Implicit function: dx x2 - sin(xy) + y² = 5xy

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Q: Find the derivative of the function f(x) = x2 - 5x + 3 at the numbers (a) 2 and (b) a. %3D

A: a. From the definition we have the following, Simplify further,

Q: What is the derivative of the function f(x)= In(3x2) ? а. f'(x)= 2 b. None of these. с. 1 f'(x)= %3D…

A: We have given that  The function is f(x) = ln(3x2)

Q: 2. f: R→ R, such that f(x) = x(2x − 3).

A: We can find the answer as below.

Q: Verify the formulas by differentiation. ∫1/(x + 1)2 dx = -1/x + 1 + C

A: Here f(x)=1x+12we have to verify that ∫1x+12 dx=-1x+1+C∫f(x) dx=∫1x+12 dxsubstitute…

Q: Find the derivative of the function. F(x) = In(4 – x®) %3D f'(x) %D

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Q: Find the differentiation and provide a complete solution a. f(x)=x2√1-x2 b. y=tan3x

A: See this diff and provide a complete solution in below

Q: b) Use the definition of the derivative to compute f'(x) for 1)f(x) = 2v-5x + 9, 2)f(x) = x sin 3x…

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Q: Find the second derivative of the function (r² + 1)(x² _ z +1) U =

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Q: Find the derivative of the function. 2 f(x) = 3F + 3cos x V X

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Q: Use the definition of the derivative to find: f(x)= 1/x^3 g(z)= z^4 - 8z^2

A: Disclaimer:  “Since you have asked multiple question, we will solve the first question for you. If…

Q: Find f(2x)dx if f(x)dx = 1. Enter the exact answer. f(2x)dx

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Q: Find the derivative of y = f(r) = VI(3r + ²). x(3x+x %3D

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Q: 1 f (x) = x4 – Vx³ + x$

A: The function is given by fx = x4-x3+x18 To evaluate: The derivative of the function.

Q: Apply the first derivative test to indentify all relative extrema. (b) f(x)=x²-2+1 (c) f(x) = cos²…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Find the linearization of the function at a. 1. f(x) = x^4 + 3x^2, a = -1 2. f(x) = sin x, a =…

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Q: The function f(x)=|x|·sin(x) is differentiable at x=0.

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Q: Let f (2) = (4z + 3) (i – 2). What is the real part of the derivative f' (1+ i)?

A: A complex-valued function consists of two parts. The part without i is referred to as the real part.…

Q: Consider the function f(x) whose second derivative is f''(x)=9x+9sin(x). If f(0)=4f(0)=4 and…

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Q: Sketch the domain of the function. f(x, y) - sin 1(x + y) y

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Q: Find the derivative. COSx a) f(x) = In %3D x2-4 4 b) g(x) = Vx + e2x + Tt

A: Given : (a) f(x)=ln(cosxx2−4)

Q: Find the derivative of the function f(x) = 9r( – 5x + 6z). %3D f'(x) =

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Q: Find ☆ f'(x) using using derivative rules. f(x) =Dx+ 2 to 11

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Q: Differentiate the function with respect to the independent variable. f(x) = 10x° cos + cos 7 f'(x)…

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Q: Q1) Compute the derivative of the function f (t)= | sin² x²dx. -t

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Q: Let f (x) = 2x* – 3x3 + 5x + 1. Find the value of df-1 at x = 1. dx

A: We have given function;

Q: Compute the Derivative f(x)=5x^pi+7.3x^8+pi^8 f'(x)=?

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Q: Consider the function f(x) whose second derivative is f''(x) = 9x + 10 sin(x). If f(0) = 3 and f'(0)…

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