Solve (m^frac{6{5}})^frac{2{5}}

$$( m ^ { \frac { 6 } { 5 } } ) ^ { \frac { 2 } { 5 } }$$

Differentiate w.r.t. m

$$\frac{12}{25m^{\frac{13}{25}}}$$

Steps Using Chain Rule

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).

$$\frac{2}{5}\left(m^{\frac{6}{5}}\right)^{\frac{2}{5}-1}\frac{\mathrm{d}}{\mathrm{d}m}(m^{\frac{6}{5}})$$

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}.

$$\frac{2}{5}\left(m^{\frac{6}{5}}\right)^{-\frac{3}{5}}\times \frac{6}{5}m^{\frac{6}{5}-1}$$

Simplify.

$$\frac{12}{25}\sqrt[5]{m}\left(m^{\frac{6}{5}}\right)^{-\frac{3}{5}}$$

Evaluate

$$m^{\frac{12}{25}}$$