Solve -5u^4*3u^2

$$- 5 u ^ { 4 } \cdot 3 u ^ { 2 }$$

Evaluate

$$-15u^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$-5u^{6}\times 3$$

Multiply -5 and 3 to get -15.

$$-15u^{6}$$

Differentiate w.r.t. u

$$-90u^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}u}(-5u^{6}\times 3)$$

Multiply -5 and 3 to get -15.

$$\frac{\mathrm{d}}{\mathrm{d}u}(-15u^{6})$$

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

$$6\left(-15\right)u^{6-1}$$

Multiply 6 times -15.

$$-90u^{6-1}$$

Subtract 1 from 6.

$$-90u^{5}$$