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Popular >

derivative of (xx^2cos(x))

Solution

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

Solution

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

Solution steps

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

Simplify

(x) x^{2} cos (x) : x^{3} cos (x)

= \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)

Graph

Popular Examples

limit as x approaches 0 of (1+2x)^{6/x}

x \to 0 lim ((1 + 2 x)^{\frac{6}{x}})

sum from n=2 to infinity of ln(ln(n))

n = 2 \sum \infty ln (ln (n))

limit as x approaches 3 of sqrt(3x-5)

x \to 3 lim (3 x - 5)

integral of+tln(t+5)

\int + t ln (t + 5) d t

derivative of 3/(2+tan(x))

\frac{d}{d x} (\frac{3}{2 + tan ( x )})

Frequently Asked Questions (FAQ)

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