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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Popular Examples

tangent of f(x)=(36x)/(x^2+36),(-3,-12/5)tangent of

f (x) = \frac{36 x}{x ^{2} + 36}, (- 3, - \frac{12}{5})

derivative of (sin(x+cos(x))sec(x)dx)

\frac{d}{d x} ((sin (x) + cos (x)) sec (x) d x)

derivative of (6x/(sqrt(x^2+2)))

\frac{d}{d x} (\frac{6 x}{x ^{2} + 2})

integral of t^2-cos(2pi)t

\int t^{2} - cos (2 π) t d t

integral of sin^2(t

\int sin^{2} (d) t

Frequently Asked Questions (FAQ)

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