Solve -a^2/(-a^8)*a

$$\frac { - a ^ { 2 } } { ( - a ^ { 8 } ) } \cdot a$$

Evaluate

$$\frac{1}{a^{5}}$$

Solution Steps

Express \frac{-a^{2}}{-a^{8}}a as a single fraction.

$$\frac{\left(-a^{2}\right)a}{-a^{8}}$$

Cancel out a in both numerator and denominator.

$$\frac{-a^{2}}{-a^{7}}$$

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

$$\frac{1}{a^{5}}$$

Differentiate w.r.t. a

$$-\frac{5}{a^{6}}$$

Steps Using Chain Rule

Express \frac{-a^{2}}{-a^{8}}a as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{\left(-a^{2}\right)a}{-a^{8}})$$

Cancel out a in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{-a^{2}}{-a^{7}})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{a^{5}})$$

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).

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

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}.

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

Simplify.

$$-5a^{4}\left(a^{5}\right)^{-2}$$