What is (\partial)/(\partial x)(\sqrt[4]{6x^2+4}) ?

The answer to (\partial)/(\partial x)(\sqrt[4]{6x^2+4}) is (3x)/((6x^2+4)^{3/4)}

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(\partial)/(\partial x)(\sqrt[4]{6x^2+4})

\frac{3 x}{( 6 x ^{2} + 4 ) ^{\frac{3}{4}}}

Solution steps

Apply the chain rule:

\frac{1}{4 ( 6 x ^{2} + 4 ) ^{\frac{3}{4}}} \frac{\partial}{\partial x} (6 x^{2} + 4)

= \frac{1}{4 ( 6 x ^{2} + 4 ) ^{\frac{3}{4}}} \frac{\partial}{\partial x} (6 x^{2} + 4)

\frac{\partial}{\partial x} (6 x^{2} + 4) = 12 x

= \frac{1}{4 ( 6 x ^{2} + 4 ) ^{\frac{3}{4}}} \cdot 12 x

Simplify

\frac{1}{4 ( 6 x ^{2} + 4 ) ^{\frac{3}{4}}} \cdot 12 x : \frac{3 x}{( 6 x ^{2} + 4 ) ^{\frac{3}{4}}}

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

\frac{7}{x + 4}

\int x^{3} e^{x^{4} + 5} d x

y + y^{4} = (y^{6} + 3 x) y^{^{'}}

cos (x) y^{^{'}} - sin (x) y = 0

What is (\partial)/(\partial x)(\sqrt[4]{6x^2+4}) ?
The answer to (\partial)/(\partial x)(\sqrt[4]{6x^2+4}) is (3x)/((6x^2+4)^{3/4)}