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Popular >

derivative of x^3*cos(x)

Solution

\frac{d}{d x} (x^{3} \cdot cos (x))

Solution

3 x^{2} cos (x) - x^{3} sin (x)

Solution steps

\frac{d}{d x} (x^{3} cos (x))

Apply the Product Rule:

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

f = x^{3}, g = cos (x)

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

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

\frac{d}{d x} (cos (x)) = - sin (x)

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

Simplify

= 3 x^{2} cos (x) - x^{3} sin (x)

Popular Examples

derivative of 3x^{2/3}-6x^{1/3}+x^{-1/3}

\frac{d}{d x} (3 x^{\frac{2}{3}} - 6 x^{\frac{1}{3}} + x^{- \frac{1}{3}})

derivative of 1/2 xsin(x)

\frac{d}{d x} (\frac{1}{2} x sin (x))

integral of 9tsec^2(2t)

\int 9 t sec^{2} (2 t) d t

integral of 7sin^2(x)cos^3(x)

\int 7 sin^{2} (x) cos^{3} (x) d x

sum from n=0 to infinity of (8^n)/(n!)

n = 0 \sum \infty \frac{8 ^{n}}{n !}

Frequently Asked Questions (FAQ)

What is the derivative of x^3*cos(x) ?
The derivative of x^3*cos(x) is 3x^2cos(x)-x^3sin(x)
What is the first derivative of x^3*cos(x) ?
The first derivative of x^3*cos(x) is 3x^2cos(x)-x^3sin(x)