Solve -3/16a^2*(-4)a^3

$$- \frac { 3 } { 16 } a ^ { 2 } \cdot ( - 4 ) a ^ { 3 }$$

Evaluate

$$\frac{3a^{5}}{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$-\frac{3}{16}a^{5}\left(-4\right)$$

Multiply -\frac{3}{16} and -4 to get \frac{3}{4}.

$$\frac{3}{4}a^{5}$$

Differentiate w.r.t. a

$$\frac{15a^{4}}{4}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-\frac{3}{16}a^{5}\left(-4\right))$$

Multiply -\frac{3}{16} and -4 to get \frac{3}{4}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{3}{4}a^{5})$$

The derivative of ax^{n} is nax^{n-1}.

$$5\times \frac{3}{4}a^{5-1}$$

Multiply 5 times \frac{3}{4}.

$$\frac{15}{4}a^{5-1}$$

Subtract 1 from 5.

$$\frac{15}{4}a^{4}$$