Solve 20x^8:2x^6=

$$20 x ^ { 8 } : 2 x ^ { 6 } =$$

Evaluate

$$10x^{14}$$

Solution Steps

Divide 20x^{8} by 2 to get 10x^{8}.

$$10x^{8}x^{6}$$

To multiply powers of the same base, add their exponents. Add 8 and 6 to get 14.

$$10x^{14}$$

Differentiate w.r.t. x

$$140x^{13}$$

Steps Using Definition of a Derivative

Divide 20x^{8} by 2 to get 10x^{8}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10x^{8}x^{6})$$

To multiply powers of the same base, add their exponents. Add 8 and 6 to get 14.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10x^{14})$$

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

$$14\times 10x^{14-1}$$

Multiply 14 times 10.

$$140x^{14-1}$$

Subtract 1 from 14.

$$140x^{13}$$