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Popular >

derivative of \sqrt[4]{xy}

Solution

Solution

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

Solution steps

Apply the chain rule:

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

= \frac{1}{4 ( x y ) ^{\frac{3}{4}}} \frac{d}{d x} (x y)

\frac{d}{d x} (x y) = y + x \frac{d y}{d x}

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

Simplify

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

= \frac{y + x \frac{d y}{d x}}{4 ( x y ) ^{\frac{3}{4}}}

Popular Examples

integral from 0 to 1 of arcsin(x)

\int_{0}^{1} arcsin (x) d x

derivative of x^{4pi}

\frac{d}{d x} (x^{4 π})

(\partial)/(\partial x)(y^{1/3}x^3)

\frac{\partial}{\partial x} (y^{\frac{1}{3}} x^{3})

\frac{d}{d v} (\frac{u}{v})

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

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

Frequently Asked Questions (FAQ)

What is the derivative of \sqrt[4]{xy} ?
The derivative of \sqrt[4]{xy} is (y+x\frac{dy)/(dx)}{4(xy)^{3/4}}
What is the first derivative of \sqrt[4]{xy} ?
The first derivative of \sqrt[4]{xy} is (y+x\frac{dy)/(dx)}{4(xy)^{3/4}}