Solve 0.8x^6*0.64x^12

$$0.8 { x }^{ 6 } \times 0.64 { x }^{ 12 }$$

Evaluate

$$\frac{64x^{18}}{125}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 12 to get 18.

$$0.8x^{18}\times 0.64$$

Multiply 0.8 and 0.64 to get 0.512.

$$0.512x^{18}$$

Differentiate w.r.t. x

$$\frac{1152x^{17}}{125}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 6 and 12 to get 18.

$$\frac{\mathrm{d}}{\mathrm{d}x}(0.8x^{18}\times 0.64)$$

Multiply 0.8 and 0.64 to get 0.512.

$$\frac{\mathrm{d}}{\mathrm{d}x}(0.512x^{18})$$

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

$$18\times 0.512x^{18-1}$$

Multiply 18 times 0.512.

$$9.216x^{18-1}$$

Subtract 1 from 18.

$$9.216x^{17}$$