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

$$( 3 x ) ( - 5 x ) ( - x )$$

Evaluate

$$15x^{3}$$

Solution Steps

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

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

Multiply 3 and -5 to get -15.

$$-15x^{2}\left(-x\right)$$

Multiply -15 and -1 to get 15.

$$15x^{2}x$$

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

$$15x^{3}$$

Differentiate w.r.t. x

$$45x^{2}$$

Steps Using Definition of a Derivative

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

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

Multiply 3 and -5 to get -15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-15x^{2}\left(-x\right))$$

Multiply -15 and -1 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15x^{2}x)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(15x^{3})$$

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

$$3\times 15x^{3-1}$$

Multiply 3 times 15.

$$45x^{3-1}$$

Subtract 1 from 3.

$$45x^{2}$$