Solve 3x^3*(-2x^2)=

$$3 x ^ { 3 } \cdot ( - 2 x ^ { 2 } ) =$$

Evaluate

$$-6x^{5}$$

Solution Steps

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

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

Multiply 3 and -2 to get -6.

$$-6x^{5}$$

Differentiate w.r.t. x

$$-30x^{4}$$

Steps Using Definition of a Derivative

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

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

Multiply 3 and -2 to get -6.

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

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

$$5\left(-6\right)x^{5-1}$$

Multiply 5 times -6.

$$-30x^{5-1}$$

Subtract 1 from 5.

$$-30x^{4}$$