What is the derivative of f(x)=x^3sin^2(x) ?

The derivative of f(x)=x^3sin^2(x) is 3x^2sin^2(x)+sin(2x)x^3

What is the first derivative of f(x)=x^3sin^2(x) ?

The first derivative of f(x)=x^3sin^2(x) is 3x^2sin^2(x)+sin(2x)x^3

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derivative of

f (x) = x^{3} sin^{2} (x)

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

What is the derivative of f(x)=x^3sin^2(x) ?
The derivative of f(x)=x^3sin^2(x) is 3x^2sin^2(x)+sin(2x)x^3
What is the first derivative of f(x)=x^3sin^2(x) ?
The first derivative of f(x)=x^3sin^2(x) is 3x^2sin^2(x)+sin(2x)x^3