What is the derivative of sqrt(\sqrt{4x+3)} ?

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

What is the first derivative of sqrt(\sqrt{4x+3)} ?

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

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derivative of

4 x + 3

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

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{2 4 x + 3} \cdot \frac{2}{4 x + 3}

Simplify

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

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

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