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Popular >

derivative of y=x^5sin^2(2x)

Solution

derivative of

y = x^{5} sin^{2} (2 x)

Solution

5 x^{4} sin^{2} (2 x) + 2 sin (4 x) x^{5}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x^{5}) = 5 x^{4}

\frac{d}{d x} (sin^{2} (2 x)) = 2 sin (4 x)

= 5 x^{4} sin^{2} (2 x) + 2 sin (4 x) x^{5}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of y=x^5sin^2(2x) ?
The derivative of y=x^5sin^2(2x) is 5x^4sin^2(2x)+2sin(4x)x^5
What is the first derivative of y=x^5sin^2(2x) ?
The first derivative of y=x^5sin^2(2x) is 5x^4sin^2(2x)+2sin(4x)x^5