Solve (u^frac{7{10}})^5

$$( u ^ { \frac { 7 } { 10 } } ) ^ { 5 }$$

Differentiate w.r.t. u

$$\frac{7u^{\frac{5}{2}}}{2}$$

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).

$$5\left(u^{\frac{7}{10}}\right)^{5-1}\frac{\mathrm{d}}{\mathrm{d}u}(u^{\frac{7}{10}})$$

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}.

$$5\left(u^{\frac{7}{10}}\right)^{4}\times \frac{7}{10}u^{\frac{7}{10}-1}$$

Simplify.

$$\frac{7}{2}u^{-\frac{3}{10}}\left(u^{\frac{7}{10}}\right)^{4}$$

Evaluate

$$u^{\frac{7}{2}}$$