Solve (u^2)^-3

$$( u ^ { 2 } ) ^ { - 3 }$$

Evaluate

$$\frac{1}{u^{6}}$$

Steps for Raising Power to Another Power

Use the rules of exponents to simplify the expression.

$$\left(u^{2}\right)^{-3}$$

To raise a power to another power, multiply the exponents.

$$u^{2\left(-3\right)}$$

Multiply 2 times -3.

$$\frac{1}{u^{6}}$$

Differentiate w.r.t. u

$$-\frac{6}{u^{7}}$$

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).

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

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}.

$$-3\left(u^{2}\right)^{-4}\times 2u^{2-1}$$

Simplify.

$$-6u^{1}\left(u^{2}\right)^{-4}$$

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

$$-6u\left(u^{2}\right)^{-4}$$