Solve (3x^2)(-4x^3)

$$( 3 x ^ { 2 } ) ( - 4 x ^ { 3 } )$$

Evaluate

$$-12x^{5}$$

Solution Steps

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

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

Multiply 3 and -4 to get -12.

$$-12x^{5}$$

Differentiate w.r.t. x

$$-60x^{4}$$

Steps Using Definition of a Derivative

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

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

Multiply 3 and -4 to get -12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-12x^{5})$$

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

$$5\left(-12\right)x^{5-1}$$

Multiply 5 times -12.

$$-60x^{5-1}$$

Subtract 1 from 5.

$$-60x^{4}$$