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

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

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

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

Solution steps

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (4 x^{2} + 2) = 8 x

= \frac{1}{4 ( 4 x ^{2} + 2 ) ^{\frac{3}{4}}} \cdot 8 x

Simplify

\frac{1}{4 ( 4 x ^{2} + 2 ) ^{\frac{3}{4}}} \cdot 8 x : \frac{2 x}{( 4 x ^{2} + 2 ) ^{\frac{3}{4}}}

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

\int_{0}^{7} \frac{8}{9 x ^{2} + 10 x + 1} d x

\frac{\partial}{\partial x} (e^{3 y} cos (- 3 x))

y = e^{x}, y = 9 - e^{x}, x = - 1, x = 1

(sin (ln (t)))^{2}

y^{^{'}} = 4 y (1 - \frac{y}{4})

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