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

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

Evaluate

$$30x^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

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

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

$$-5x^{6}\times 2\left(-3\right)$$

Multiply -5 and 2 to get -10.

$$-10x^{6}\left(-3\right)$$

Multiply -10 and -3 to get 30.

$$30x^{6}$$

Differentiate w.r.t. x

$$180x^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

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

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-5x^{6}\times 2\left(-3\right))$$

Multiply -5 and 2 to get -10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-10x^{6}\left(-3\right))$$

Multiply -10 and -3 to get 30.

$$\frac{\mathrm{d}}{\mathrm{d}x}(30x^{6})$$

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

$$6\times 30x^{6-1}$$

Multiply 6 times 30.

$$180x^{6-1}$$

Subtract 1 from 6.

$$180x^{5}$$