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

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

Evaluate

$$-2x^{5}$$

Solution Steps

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

$$-4x^{5}\times \frac{1}{2}$$

Multiply -4 and \frac{1}{2} 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 3 and 2 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-4x^{5}\times \frac{1}{2})$$

Multiply -4 and \frac{1}{2} 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.

$$-10x^{4}$$