Solve 10x^3*(-16x^2)

$$10 { x }^{ 3 } \times (-16 { x }^{ 2 } )$$

Evaluate

$$-160x^{5}$$

Solution Steps

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

$$10x^{5}\left(-16\right)$$

Multiply 10 and -16 to get -160.

$$-160x^{5}$$

Differentiate w.r.t. x

$$-800x^{4}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(10x^{5}\left(-16\right))$$

Multiply 10 and -16 to get -160.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-160x^{5})$$

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

$$5\left(-160\right)x^{5-1}$$

Multiply 5 times -160.

$$-800x^{5-1}$$

Subtract 1 from 5.

$$-800x^{4}$$