Solve (1/4x^2)(-8x^3)

$$( \frac{ 1 }{ 4 } { x }^{ 2 } )(-8 { x }^{ 3 } )$$

Evaluate

$$-2x^{5}$$

Solution Steps

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

$$\frac{1}{4}x^{5}\left(-8\right)$$

Multiply \frac{1}{4} and -8 to get -2.

$$-2x^{5}$$

Differentiate w.r.t. x

$$-10x^{4}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{4}x^{5}\left(-8\right))$$

Multiply \frac{1}{4} and -8 to get -2.

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

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

$$5\left(-2\right)x^{5-1}$$

Multiply 5 times -2.

$$-10x^{5-1}$$

Subtract 1 from 5.

$$-10x^{4}$$