What is the derivative of x^2sin^2(5x) ?

The derivative of x^2sin^2(5x) is 2xsin^2(5x)+5sin(10x)x^2

What is the first derivative of x^2sin^2(5x) ?

The first derivative of x^2sin^2(5x) is 2xsin^2(5x)+5sin(10x)x^2

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

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