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derivative of \sqrt[3]{cos(x})

Solution

Solution

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

Solution steps

Apply the chain rule:

\frac{1}{3 ( cos ( x ) ) ^{\frac{2}{3}}} \frac{d}{d x} (cos (x))

= \frac{1}{3 ( cos ( x ) ) ^{\frac{2}{3}}} \frac{d}{d x} (cos (x))

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

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

Simplify

\frac{1}{3 cos ^{\frac{2}{3}} ( x )} (- sin (x)) : - \frac{sin ( x )}{3 cos ^{\frac{2}{3}} ( x )}

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

Popular Examples

(\partial)/(\partial y)(y^2e^{xy-3})

\frac{\partial}{\partial y} (y^{2} e^{x y - 3})

limit as x approaches-5 of 3/(x+5)

x \to - 5 lim (\frac{3}{x + 5})

integral of 1/(-2y)

\int \frac{1}{- 2 y} d y

derivative of y=3sin((xpi)/(90))derivative of

y = 3 sin (\frac{x π}{90})

integral of 3xe^{5x^2}

\int 3 x e^{5 x^{2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of \sqrt[3]{cos(x}) ?
The derivative of \sqrt[3]{cos(x}) is -(sin(x))/(3cos^{2/3)(x)}
What is the first derivative of \sqrt[3]{cos(x}) ?
The first derivative of \sqrt[3]{cos(x}) is -(sin(x))/(3cos^{2/3)(x)}