Solve (w^2)^frac{-3{10}}

$$( w ^ { 2 } ) ^ { \frac { - 3 } { 10 } }$$

Differentiate w.r.t. w

$$-\frac{3|w|}{5w^{\frac{13}{5}}}$$

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).

$$-\frac{3}{10}\left(w^{2}\right)^{-\frac{3}{10}-1}\frac{\mathrm{d}}{\mathrm{d}w}(w^{2})$$

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}.

$$-\frac{3}{10}\left(w^{2}\right)^{-\frac{13}{10}}\times 2w^{2-1}$$

Simplify.

$$-\frac{3}{5}w^{1}\left(w^{2}\right)^{-\frac{13}{10}}$$

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

$$-\frac{3}{5}w\left(w^{2}\right)^{-\frac{13}{10}}$$

Evaluate

$$\frac{1}{\left(|w|\right)^{\frac{3}{5}}}$$