Solve 4*x^2*-8x^3

$$4 \times { x }^{ 2 } \times -8 { x }^{ 3 }$$

Evaluate

$$-32x^{5}$$

Solution Steps

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

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

Multiply 4 and -8 to get -32.

$$-32x^{5}$$

Differentiate w.r.t. x

$$-160x^{4}$$

Steps Using Definition of a Derivative

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

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

Multiply 4 and -8 to get -32.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-32x^{5})$$

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

$$5\left(-32\right)x^{5-1}$$

Multiply 5 times -32.

$$-160x^{5-1}$$

Subtract 1 from 5.

$$-160x^{4}$$