What is the derivative of \sqrt[4]{2x+16} ?

The derivative of \sqrt[4]{2x+16} is 1/(2(2x+16)^{3/4)}

What is the first derivative of \sqrt[4]{2x+16} ?

The first derivative of \sqrt[4]{2x+16} is 1/(2(2x+16)^{3/4)}

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\frac{1}{2 ( 2 x + 16 ) ^{\frac{3}{4}}}

Solution steps

Apply the chain rule:

\frac{1}{4 ( 2 x + 16 ) ^{\frac{3}{4}}} \frac{d}{d x} (2 x + 16)

= \frac{1}{4 ( 2 x + 16 ) ^{\frac{3}{4}}} \frac{d}{d x} (2 x + 16)

\frac{d}{d x} (2 x + 16) = 2

= \frac{1}{4 ( 2 x + 16 ) ^{\frac{3}{4}}} \cdot 2

Simplify

\frac{1}{4 ( 2 x + 16 ) ^{\frac{3}{4}}} \cdot 2 : \frac{1}{2 ( 2 x + 16 ) ^{\frac{3}{4}}}

= \frac{1}{2 ( 2 x + 16 ) ^{\frac{3}{4}}}

x \to \infty lim (ln (- x))

2^{^{'}}

\frac{d y}{d x} = \frac{( e ^{x - y} )}{( 1 + e ^{x} )}

y^{^{'}} + a \cdot y - b = 0

y = 9 x e^{x}, (0, 0)

What is the derivative of \sqrt[4]{2x+16} ?
The derivative of \sqrt[4]{2x+16} is 1/(2(2x+16)^{3/4)}
What is the first derivative of \sqrt[4]{2x+16} ?
The first derivative of \sqrt[4]{2x+16} is 1/(2(2x+16)^{3/4)}