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Popular >

derivative of cos^3(x+sin^3(x))

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Popular Examples

limit as x approaches infinity of 3/2

x \to \infty lim (\frac{3}{2})

integral from 0 to pi of 2pix(sin(x))

\int_{0}^{π} 2 π x (sin (x)) d x

integral of cos(2+t)

\int cos (2 + t) d t

(x^2+1)y^'+3x(y-1)=0,y(0)=5

(x^{2} + 1) y^{^{'}} + 3 x (y - 1) = 0, y (0) = 5

integral from 0 to infinity of e^{-x^2}

\int_{0}^{\infty} e^{- x^{2}} d x

Frequently Asked Questions (FAQ)

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