Solve 2(-3x)(5x^3)

$$2 ( - 3 x ) ( 5 x ^ { 3 } )$$

Evaluate

$$-30x^{4}$$

Solution Steps

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

$$2\left(-3\right)x^{4}\times 5$$

Multiply 2 and -3 to get -6.

$$-6x^{4}\times 5$$

Multiply -6 and 5 to get -30.

$$-30x^{4}$$

Differentiate w.r.t. x

$$-120x^{3}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(2\left(-3\right)x^{4}\times 5)$$

Multiply 2 and -3 to get -6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-6x^{4}\times 5)$$

Multiply -6 and 5 to get -30.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-30x^{4})$$

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

$$4\left(-30\right)x^{4-1}$$

Multiply 4 times -30.

$$-120x^{4-1}$$

Subtract 1 from 4.

$$-120x^{3}$$