Solve -5u(-5u)(-5u)(-5u)(-5u)

$$- 5 u ( - 5 u ) ( - 5 u ) ( - 5 u ) ( - 5 u )$$

Evaluate

$$-3125u^{5}$$

Solution Steps

Multiply u and u to get u^{2}.

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

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

$$-5u^{3}\left(-5\right)\left(-5\right)\left(-5\right)u\left(-5\right)u$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

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

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

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

Multiply -5 and -5 to get 25.

$$25u^{5}\left(-5\right)\left(-5\right)\left(-5\right)$$

Multiply 25 and -5 to get -125.

$$-125u^{5}\left(-5\right)\left(-5\right)$$

Multiply -125 and -5 to get 625.

$$625u^{5}\left(-5\right)$$

Multiply 625 and -5 to get -3125.

$$-3125u^{5}$$

Differentiate w.r.t. u

$$-15625u^{4}$$

Steps Using Definition of a Derivative

Multiply u and u to get u^{2}.

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

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

$$\frac{\mathrm{d}}{\mathrm{d}u}(-5u^{3}\left(-5\right)\left(-5\right)\left(-5\right)u\left(-5\right)u)$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}u}(-5u^{4}\left(-5\right)\left(-5\right)\left(-5\right)\left(-5\right)u)$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

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

Multiply -5 and -5 to get 25.

$$\frac{\mathrm{d}}{\mathrm{d}u}(25u^{5}\left(-5\right)\left(-5\right)\left(-5\right))$$

Multiply 25 and -5 to get -125.

$$\frac{\mathrm{d}}{\mathrm{d}u}(-125u^{5}\left(-5\right)\left(-5\right))$$

Multiply -125 and -5 to get 625.

$$\frac{\mathrm{d}}{\mathrm{d}u}(625u^{5}\left(-5\right))$$

Multiply 625 and -5 to get -3125.

$$\frac{\mathrm{d}}{\mathrm{d}u}(-3125u^{5})$$

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

$$5\left(-3125\right)u^{5-1}$$

Multiply 5 times -3125.

$$-15625u^{5-1}$$

Subtract 1 from 5.

$$-15625u^{4}$$