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

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

Evaluate

$$-15x$$

Solution Steps

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

$$5x^{1}\left(-3\right)$$

Calculate x to the power of 1 and get x.

$$5x\left(-3\right)$$

Multiply 5 and -3 to get -15.

$$-15x$$

Differentiate w.r.t. x

$$-15$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{1}\left(-3\right))$$

Calculate x to the power of 1 and get x.

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

Multiply 5 and -3 to get -15.

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

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

$$-15x^{1-1}$$

Subtract 1 from 1.

$$-15x^{0}$$

For any term t except 0, t^{0}=1.

$$-15$$