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Popular >

derivative of f(x)=x^3cos(x)

Solution

derivative of

f (x) = x^{3} 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

integral of e^{-r^2}*r

\int e^{- r^{2}} \cdot r d r

integral from 0 to 1 of sin^3(pi/2 x)

\int_{0}^{1} sin^{3} (\frac{π}{2} x) d x

limit as x approaches 0 of 3x^2+1

x \to 0 lim (3 x^{2} + 1)

integral from 0 to x of t(e^{2t^3}-1)

\int_{0}^{x} t (e^{2 t^{3}} - 1) d t

implicit (dy)/(dx),x^3-xy+y^2=7 implicit derivative

\frac{d y}{d x}, x^{3} - x y + y^{2} = 7

Frequently Asked Questions (FAQ)

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