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

The derivative of sqrt(x\sqrt{x\sqrt{x)}} is (7x^{3/4})/(8sqrt(x^{7/4))}

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

The first derivative of sqrt(x\sqrt{x\sqrt{x)}} is (7x^{3/4})/(8sqrt(x^{7/4))}

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derivative of

x x x

\frac{7 x ^{\frac{3}{4}}}{8 x ^{\frac{7}{4}}}

Solution steps

\frac{d}{d x} (x x x)

Apply the chain rule:

\frac{1}{2 x x x} \frac{d}{d x} (x x x)

= \frac{1}{2 x x x} \frac{d}{d x} (x x x)

\frac{d}{d x} (x x x) = \frac{7 x ^{\frac{3}{4}}}{4}

= \frac{1}{2 x x x} \cdot \frac{7 x ^{\frac{3}{4}}}{4}

Simplify

\frac{1}{2 x x x} \cdot \frac{7 x ^{\frac{3}{4}}}{4} : \frac{7 x ^{\frac{3}{4}}}{8 x ^{\frac{7}{4}}}

= \frac{7 x ^{\frac{3}{4}}}{8 x ^{\frac{7}{4}}}

\int csc^{2} (4 x) d x

y = x^{8}, y = x^{6}

y^{2} \frac{d y}{d x} = e^{x}

\int x^{\frac{1}{5}} d x

\int 54 x d x

What is the derivative of sqrt(x\sqrt{x\sqrt{x)}} ?
The derivative of sqrt(x\sqrt{x\sqrt{x)}} is (7x^{3/4})/(8sqrt(x^{7/4))}
What is the first derivative of sqrt(x\sqrt{x\sqrt{x)}} ?
The first derivative of sqrt(x\sqrt{x\sqrt{x)}} is (7x^{3/4})/(8sqrt(x^{7/4))}