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Popular >

(\partial}{\partial x}((x^4)/(6y)+\frac{12y^4)/x)

Solution

\frac{\partial}{\partial x} (\frac{x ^{4}}{6 y} + \frac{12 y ^{4}}{x})

Solution

\frac{2 x ^{3}}{3 y} - \frac{12 y ^{4}}{x ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{x ^{4}}{6 y} + \frac{12 y ^{4}}{x})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (\frac{x ^{4}}{6 y}) + \frac{\partial}{\partial x} (\frac{12 y ^{4}}{x})

\frac{\partial}{\partial x} (\frac{x ^{4}}{6 y}) = \frac{2 x ^{3}}{3 y}

\frac{\partial}{\partial x} (\frac{12 y ^{4}}{x}) = - \frac{12 y ^{4}}{x ^{2}}

= \frac{2 x ^{3}}{3 y} - \frac{12 y ^{4}}{x ^{2}}

Popular Examples

derivative of (xe^x/(x+e^x))

\frac{d}{d x} (\frac{x e ^{x}}{x + e ^{x}})

derivative of sin(x+1/(sqrt(x)))

\frac{d}{d x} (sin (x) + \frac{1}{x})

(\partial)/(\partial x)(-3sin(x))

\frac{\partial}{\partial x} (- 3 sin (x))

sum from n=2 to infinity of 1/(n^n)

n = 2 \sum \infty \frac{1}{n ^{n}}

limit as n approaches infinity of n^1

n \to \infty lim (n^{1})

Frequently Asked Questions (FAQ)

What is (\partial}{\partial x}((x^4)/(6y)+\frac{12y^4)/x) ?
The answer to (\partial}{\partial x}((x^4)/(6y)+\frac{12y^4)/x) is (2x^3)/(3y)-(12y^4)/(x^2)