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Popular >

derivative of xcos^3(x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

= 1 \cdot cos^{3} (x) + (- 3 cos^{2} (x) sin (x)) x

Simplify

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

Popular Examples

integral from 1 to 2 of sqrt(x)ln(x)

\int_{1}^{2} x ln (x) d x

derivative of e^{(-3x})

\frac{d}{d x} (e^{(- 3 x)})

taylor e^{-3z+1}+8 taylor

e^{- 3 z + 1} + 8

tangent of x^{2/3}+y^{2/3}=5,(1,8)tangent of

x^{\frac{2}{3}} + y^{\frac{2}{3}} = 5, (1, 8)

derivative of f(x)=(2x-1)/(2x+1)derivative of

f (x) = \frac{2 x - 1}{2 x + 1}

Frequently Asked Questions (FAQ)

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