Solve 1/u^-5

$$\frac { 1 } { u ^ { - 5 } }$$

Differentiate w.r.t. u

$$5u^{4}$$

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).

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

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}.

$$-\left(u^{-5}\right)^{-2}\left(-5\right)u^{-5-1}$$

Simplify.

$$5u^{-6}\left(u^{-5}\right)^{-2}$$

Evaluate

$$u^{5}$$