Solve 2u^3(-5u^4)

$$2 u ^ { 3 } ( - 5 u ^ { 4 } )$$

Evaluate

$$-10u^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$2u^{7}\left(-5\right)$$

Multiply 2 and -5 to get -10.

$$-10u^{7}$$

Differentiate w.r.t. u

$$-70u^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}u}(2u^{7}\left(-5\right))$$

Multiply 2 and -5 to get -10.

$$\frac{\mathrm{d}}{\mathrm{d}u}(-10u^{7})$$

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

$$7\left(-10\right)u^{7-1}$$

Multiply 7 times -10.

$$-70u^{7-1}$$

Subtract 1 from 7.

$$-70u^{6}$$