Mathematics, 17.10.2020 14:01 mayalp

Second derivative of y = x sinx

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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

no not all of them.

step-by-step explanation:

some of them have a square base.

Answer from: Quest

found it xd it ok yt

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