Solve 1/a^2*a^2/-a^2

$$\frac { 1 } { a ^ { 2 } } \cdot \frac { a ^ { 2 } } { - a ^ { 2 } }$$

Evaluate

$$-\frac{1}{a^{2}}$$

Steps for Raising Power to Another Power

Multiply \frac{1}{a^{2}} times \frac{a^{2}}{-a^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{a^{2}}{a^{2}\left(-a^{2}\right)}$$

Cancel out a^{2} in both numerator and denominator.

$$\frac{1}{-a^{2}}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$-\frac{1}{a^{2}}$$

Differentiate w.r.t. a

$$\frac{2}{a^{3}}$$

Steps Using Chain Rule

Multiply \frac{1}{a^{2}} times \frac{a^{2}}{-a^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{2}}{a^{2}\left(-a^{2}\right)})$$

Cancel out a^{2} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{-a^{2}})$$

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).

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

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}.

$$-\left(-a^{2}\right)^{-2}\times 2\left(-1\right)a^{2-1}$$

Simplify.

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

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

$$2a\left(-a^{2}\right)^{-2}$$