Solve 3x(-8x^7)

$$3 x ( - 8 x ^ { 7 } )$$

Evaluate

$$-24x^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 7 to get 8.

$$3x^{8}\left(-8\right)$$

Multiply 3 and -8 to get -24.

$$-24x^{8}$$

Differentiate w.r.t. x

$$-192x^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 7 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{8}\left(-8\right))$$

Multiply 3 and -8 to get -24.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-24x^{8})$$

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

$$8\left(-24\right)x^{8-1}$$

Multiply 8 times -24.

$$-192x^{8-1}$$

Subtract 1 from 8.

$$-192x^{7}$$