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Popular >

derivative of (6-x^{1/3})

Solution

\frac{d}{d x} ((6 - x)^{\frac{1}{3}})

Solution

- \frac{1}{3 ( 6 - x ) ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} ((6 - x)^{\frac{1}{3}})

Apply the chain rule:

\frac{1}{3 ( 6 - x ) ^{\frac{2}{3}}} \frac{d}{d x} (6 - x)

= \frac{1}{3 ( 6 - x ) ^{\frac{2}{3}}} \frac{d}{d x} (6 - x)

\frac{d}{d x} (6 - x) = - 1

= \frac{1}{3 ( 6 - x ) ^{\frac{2}{3}}} (- 1)

Simplify

= - \frac{1}{3 ( 6 - x ) ^{\frac{2}{3}}}

Popular Examples

integral of 3/x-4/(x^5)

\int \frac{3}{x} - \frac{4}{x ^{5}} d x

inverse oflaplace (9s)/(5(s^2+5s+11))inverse laplace

\frac{9 s}{5 ( s ^{2} + 5 s + 11 )}

derivative of x/(x-1)derivative of

\frac{x}{x - 1}

(\partial)/(\partial y)(sqrt(y-x)-z)

\frac{\partial}{\partial y} (y - x - z)

f(x)=5-3(1+x^2)^{-1}

f (x) = 5 - 3 (1 + x^{2})^{- 1}

Frequently Asked Questions (FAQ)

What is the derivative of (6-x^{1/3}) ?
The derivative of (6-x^{1/3}) is -1/(3(6-x)^{2/3)}
What is the first derivative of (6-x^{1/3}) ?
The first derivative of (6-x^{1/3}) is -1/(3(6-x)^{2/3)}