Solve (u^frac{3{8}})^2

$$( u ^ { \frac { 3 } { 8 } } ) ^ { 2 }$$

Differentiate w.r.t. u

$$\frac{3}{4\sqrt[4]{u}}$$

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).

$$2\left(u^{\frac{3}{8}}\right)^{2-1}\frac{\mathrm{d}}{\mathrm{d}u}(u^{\frac{3}{8}})$$

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}.

$$2\left(u^{\frac{3}{8}}\right)^{1}\times \frac{3}{8}u^{\frac{3}{8}-1}$$

Simplify.

$$\frac{3}{4}u^{-\frac{5}{8}}\left(u^{\frac{3}{8}}\right)^{1}$$

For any term t, t^{1}=t.

$$\frac{3}{4}u^{-\frac{5}{8}}u^{\frac{3}{8}}$$

Evaluate

$$u^{\frac{3}{4}}$$