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Popular >

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

Solution

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

Solution

10 x^{9} sin^{5} (x) + 5 sin^{4} (x) cos (x) x^{10}

Solution steps

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

Simplify

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

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

Apply the Product Rule:

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

f = x^{10}, g = sin^{5} (x)

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

\frac{d}{d x} (x^{10}) = 10 x^{9}

\frac{d}{d x} (sin^{5} (x)) = 5 sin^{4} (x) cos (x)

= 10 x^{9} sin^{5} (x) + 5 sin^{4} (x) cos (x) x^{10}

Popular Examples

integral of (e^x)/(x+1)

\int \frac{e ^{x}}{x + 1} d x

d/(dt)((sec^2(t))/(sec(t)tan(t)))

\frac{d}{d t} (\frac{sec ^{2} ( t )}{sec ( t ) tan ( t )})

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

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

(\partial)/(\partial x)(2y^2+3x)

\frac{\partial}{\partial x} (2 y^{2} + 3 x)

integral of (x^{10})/(x^2+x-2)

\int \frac{x ^{10}}{x ^{2} + x - 2} d x

Frequently Asked Questions (FAQ)

What is the derivative of (x^2sin(x)^5) ?
The derivative of (x^2sin(x)^5) is 10x^9sin^5(x)+5sin^4(x)cos(x)x^{10}
What is the first derivative of (x^2sin(x)^5) ?
The first derivative of (x^2sin(x)^5) is 10x^9sin^5(x)+5sin^4(x)cos(x)x^{10}