Solve (x^2)^-12

$$( x ^ { 2 } ) ^ { - 12 }$$

Evaluate

$$\frac{1}{x^{24}}$$

Steps for Raising Power to Another Power

Use the rules of exponents to simplify the expression.

$$\left(x^{2}\right)^{-12}$$

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

$$x^{2\left(-12\right)}$$

Multiply 2 times -12.

$$\frac{1}{x^{24}}$$

Differentiate w.r.t. x

$$-\frac{24}{x^{25}}$$

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).

$$-12\left(x^{2}\right)^{-12-1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{2})$$

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}.

$$-12\left(x^{2}\right)^{-13}\times 2x^{2-1}$$

Simplify.

$$-24x^{1}\left(x^{2}\right)^{-13}$$

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

$$-24x\left(x^{2}\right)^{-13}$$