Solve (-3x)(5x^5)

$$( - 3 x ) ( 5 x ^ { 5 } )$$

Evaluate

$$-15x^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

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

Multiply -3 and 5 to get -15.

$$-15x^{6}$$

Differentiate w.r.t. x

$$-90x^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

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

Multiply -3 and 5 to get -15.

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

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

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

Multiply 6 times -15.

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

Subtract 1 from 6.

$$-90x^{5}$$