Solve 4x^2(-5x^6)

$$4 x ^ { 2 } ( - 5 x ^ { 6 } )$$

Evaluate

$$-20x^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

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

Multiply 4 and -5 to get -20.

$$-20x^{8}$$

Differentiate w.r.t. x

$$-160x^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

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

Multiply 4 and -5 to get -20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-20x^{8})$$

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

$$8\left(-20\right)x^{8-1}$$

Multiply 8 times -20.

$$-160x^{8-1}$$

Subtract 1 from 8.

$$-160x^{7}$$