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Popular >

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

Solution

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

Solution

3 x^{2} sin^{2} (5 x) + 5 sin (10 x) x^{3}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

= 3 x^{2} sin^{2} (5 x) + 5 sin (10 x) x^{3}

Popular Examples

integral of ln(5x^2)

\int ln (5 x^{2}) d x

integral from 1 to 2 of 3sqrt(4x^2-3)

\int_{1}^{2} 3 4 x^{2} - 3 d x

area f(x)=2x,1,3 area

f (x) = 2 x, 1, 3

integral of (cos(x))/(sin^2(x)-81)

\int \frac{cos ( x )}{sin ^{2} ( x ) - 81} d x

limit as x approaches 0+of e^{sqrt(x)}

x \to 0 + lim (e^{x})

Frequently Asked Questions (FAQ)

What is the derivative of x^3sin^2(5x) ?
The derivative of x^3sin^2(5x) is 3x^2sin^2(5x)+5sin(10x)x^3
What is the first derivative of x^3sin^2(5x) ?
The first derivative of x^3sin^2(5x) is 3x^2sin^2(5x)+5sin(10x)x^3