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Popular >

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

Solution

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

Solution

2 x sin^{3} (5 x) + 15 sin^{2} (5 x) cos (5 x) x^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (sin^{3} (5 x)) = 15 sin^{2} (5 x) cos (5 x)

= 2 x sin^{3} (5 x) + 15 sin^{2} (5 x) cos (5 x) x^{2}

Popular Examples

integral of 1/(x^2sqrt(x^2-64))

\int \frac{1}{x ^{2} x ^{2} - 64} d x

integral of 1/(sqrt(t^2-8t+25))

\int \frac{1}{t ^{2} - 8 t + 25} d t

integral of e^{2x+5}

\int e^{2 x + 5} d x

(dy)/(dx)=(2x)/(y^2)

\frac{d y}{d x} = \frac{2 x}{y ^{2}}

integral of (13)/((x-3)(x^2+4))

\int \frac{13}{( x - 3 ) ( x ^{2} + 4 )} d x

Frequently Asked Questions (FAQ)

What is the derivative of x^2sin^3(5x) ?
The derivative of x^2sin^3(5x) is 2xsin^3(5x)+15sin^2(5x)cos(5x)x^2
What is the first derivative of x^2sin^3(5x) ?
The first derivative of x^2sin^3(5x) is 2xsin^3(5x)+15sin^2(5x)cos(5x)x^2