Solve (w^7)^frac{3{8}}

$$( w ^ { 7 } ) ^ { \frac { 3 } { 8 } }$$

Differentiate w.r.t. w

$$\frac{21w^{\frac{13}{8}}}{8}$$

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).

$$\frac{3}{8}\left(w^{7}\right)^{\frac{3}{8}-1}\frac{\mathrm{d}}{\mathrm{d}w}(w^{7})$$

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}.

$$\frac{3}{8}\left(w^{7}\right)^{-\frac{5}{8}}\times 7w^{7-1}$$

Simplify.

$$\frac{21}{8}w^{6}\left(w^{7}\right)^{-\frac{5}{8}}$$

Evaluate

$$w^{\frac{21}{8}}$$