Solve -2^3(-4x^6)

$$- 2 ^ { 3 } ( - 4 x ^ { 6 } )$$

Evaluate

$$32x^{6}$$

Solution Steps

Calculate 2 to the power of 3 and get 8.

$$-8\left(-4\right)x^{6}$$

Multiply -8 and -4 to get 32.

$$32x^{6}$$

Differentiate w.r.t. x

$$192x^{5}$$

Steps Using Definition of a Derivative

Calculate 2 to the power of 3 and get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-8\left(-4\right)x^{6})$$

Multiply -8 and -4 to get 32.

$$\frac{\mathrm{d}}{\mathrm{d}x}(32x^{6})$$

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

$$6\times 32x^{6-1}$$

Multiply 6 times 32.

$$192x^{6-1}$$

Subtract 1 from 6.

$$192x^{5}$$