Solve frac{sqrt[5]{b}sqrt{b}}{b}

$$\frac{ \sqrt[ 5 ]{ b } \sqrt{ b } }{ b }$$

Differentiate w.r.t. b

$$-\frac{3}{10b^{\frac{13}{10}}}$$

Steps Using Chain Rule

Factor the expressions that are not already factored in \frac{\sqrt[5]{b}\sqrt{b}}{b}.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{\sqrt[5]{b}\sqrt{b}}{b})$$

Cancel out \sqrt[5]{b}\sqrt{b} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{1}{b^{\frac{3}{10}}})$$

If F is the composition of two differentiable functions f\left(u\right) and u=g\left(x\right), that is, if F\left(x\right)=f\left(g\left(x\right)\right), then the derivative of F is the derivative of f with respect to u times the derivative of g with respect to x, that is, \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right).

$$-\left(b^{\frac{3}{10}}\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}b}(b^{\frac{3}{10}})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$-\left(b^{\frac{3}{10}}\right)^{-2}\times \frac{3}{10}b^{\frac{3}{10}-1}$$

Simplify.

$$-\frac{3}{10}b^{-\frac{7}{10}}\left(b^{\frac{3}{10}}\right)^{-2}$$

Evaluate

$$\frac{1}{b^{\frac{3}{10}}}$$