Mathematics, 17.10.2020 14:01 mayalp

Second derivative of y = x sinx

Answers: 3

Show answers

Answers

Answer from: john9727

$\displaystyle \frac{d^2y}{dx^2} = 2 \cos (x) - x \sin (x)$

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Derivative Property [Addition/Subtraction]: $\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]$

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Derivative Rule [Product Rule]: $\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle y = x \sin (x)$

Step 2: Differentiate

Derivative Rule [Product Rule]: $\displaystyle y' = (x)' \sin (x) + x \big( \sin (x) \big)'$ Basic Power Rule: $\displaystyle y' = \sin (x) + x \big( \sin (x) \big)'$ Trigonometric Differentiation: $\displaystyle y' = \sin (x) + x \cos (x)$ Derivative Property [Addition/Subtraction]: $\displaystyle y'' = \frac{d}{dx}[\sin (x)] + \frac{d}{dx}[x \cos (x)]$ Derivative Rule [Product Rule]: $\displaystyle y'' = \frac{d}{dx}[\sin (x)] + (x)' \cos (x) + x \big( \cos (x) \big)'$ Trigonometric Differentiation: $\displaystyle y'' = \cos (x) + (x)' \cos (x) - x \sin (x)$ Basic Power Rule: $\displaystyle y'' = \cos (x) + \cos (x) - x \sin (x)$ Simplify: $\displaystyle y'' = 2\cos (x) - x \sin (x)$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Answer from: Quest

step-by-step explanation:

because 1/3 is a fraction. we can tell because there is a divisor symbol between the 1 and the 3. if we were to add 2 fractions together, we would add the numerators, which is the number on top, but not the denominators, which is the number on the bottom

1/3+1/3=2/3

hope this !

Answer from: Quest

isaiah walks 3 miles due north, turns and then 5 miles due east. how far is he from his starting point?

a^2 + b^2 = c^2

let c = distance from starting point.

(3)^2 + (5)^2 = c^2

9 + 25 = c^2

34 = c^2

sqrt{34} = sqrt{c^2}

sqrt{34} = c

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 18:00, corrineikerd

Simplify the expression. -2/5(10+15m-20n)

Answers: 1

continue

Mathematics, 21.06.2019 19:30, emcarrell

Okay so i didn't get this problem petro bought 8 tickets to a basketball game he paid a total of $200 write an equation to determine whether each ticket cost $26 or $28 so i didn't get this question so yeahyou have a good day.

Answers: 1

continue

Mathematics, 21.06.2019 22:00, d0ram0UsE

Rick is driving to his uncles house in greenville, which is 120 miles from ricks town .after covering x miles rick she's a sign stating that greensville is 20 miles away. which equation when solved will give the value of x. a: x+120 = 20 b: x x120 =20 c: x +20 equals 120 d: x x20= 120

Answers: 3

continue

Mathematics, 22.06.2019 00:10, Anaaguayo7406

Change negative exponents to positive, then solve

Answers: 1

continue

You know the right answer?

Second derivative of y = x sinx...