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Popular >

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

Solution

\frac{d}{d x} (3 sin (x))

Solution

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

Solution steps

\frac{d}{d x} (3 sin (x))

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

Popular Examples

integral of 1/(1+u^2)

\int \frac{1}{1 + u ^{2}} d u

integral of (x^3)/((1+x^4))

\int \frac{x ^{3}}{( 1 + x ^{4} )} d x

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

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

integral from 0 to 1 of 2piy(y-y^2)

\int_{0}^{1} 2 π y (y - y^{2}) d y

(\partial)/(\partial x)(sin(pixy))

\frac{\partial}{\partial x} (sin (p i x y))

Frequently Asked Questions (FAQ)

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