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Popular Calculus >

derivative of x^3*sin^2(5x)

Solution

\frac{d}{d x} (x^{3} \cdot sin^{2} (5 x))

Solution

3 x^{2} sin^{2} (5 x) + 5 sin (10 x) x^{3}

Solution steps

\frac{d}{d x} (x^{3} sin^{2} (5 x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{3}, g = sin^{2} (5 x)

= \frac{d}{d x} (x^{3}) sin^{2} (5 x) + \frac{d}{d x} (sin^{2} (5 x)) x^{3}

\frac{d}{d x} (x^{3}) = 3 x^{2}

\frac{d}{d x} (sin^{2} (5 x)) = 5 sin (10 x)

= 3 x^{2} sin^{2} (5 x) + 5 sin (10 x) x^{3}

Graph

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\int 3 x - x^{2} d x

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d/(dt)(sqrt(3t))

\frac{d}{d t} (3 t)

derivative of (x^n/n)

\frac{d}{d x} (\frac{x ^{n}}{n})

Frequently Asked Questions (FAQ)

What is the derivative of x^3*sin^2(5x) ?
The derivative of x^3*sin^2(5x) is 3x^2sin^2(5x)+5sin(10x)x^3
What is the first derivative of x^3*sin^2(5x) ?
The first derivative of x^3*sin^2(5x) is 3x^2sin^2(5x)+5sin(10x)x^3