Solve -5x^28x^2

$$-5 { x }^{ 2 } 8 { x }^{ 2 }$$

Evaluate

$$-40x^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$-5x^{4}\times 8$$

Multiply -5 and 8 to get -40.

$$-40x^{4}$$

Differentiate w.r.t. x

$$-160x^{3}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

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

Multiply -5 and 8 to get -40.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-40x^{4})$$

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

$$4\left(-40\right)x^{4-1}$$

Multiply 4 times -40.

$$-160x^{4-1}$$

Subtract 1 from 4.

$$-160x^{3}$$