Solve (3/4k^2)(-1/2k)=

$$( \frac { 3 } { 4 } k ^ { 2 } ) ( - \frac { 1 } { 2 } k ) =$$

Evaluate

$$-\frac{3k^{3}}{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{3}{4}k^{3}\left(-\frac{1}{2}\right)$$

Multiply \frac{3}{4} and -\frac{1}{2} to get -\frac{3}{8}.

$$-\frac{3}{8}k^{3}$$

Differentiate w.r.t. k

$$-\frac{9k^{2}}{8}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{3}{4}k^{3}\left(-\frac{1}{2}\right))$$

Multiply \frac{3}{4} and -\frac{1}{2} to get -\frac{3}{8}.

$$\frac{\mathrm{d}}{\mathrm{d}k}(-\frac{3}{8}k^{3})$$

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

$$3\left(-\frac{3}{8}\right)k^{3-1}$$

Multiply 3 times -\frac{3}{8}.

$$-\frac{9}{8}k^{3-1}$$

Subtract 1 from 3.

$$-\frac{9}{8}k^{2}$$