Solve 20x^8div4x^2

$$20 { x }^{ 8 } \div 4 { x }^{ 2 }$$

Evaluate

$$5x^{10}$$

Solution Steps

Divide 20x^{8} by 4 to get 5x^{8}.

$$5x^{8}x^{2}$$

To multiply powers of the same base, add their exponents. Add 8 and 2 to get 10.

$$5x^{10}$$

Differentiate w.r.t. x

$$50x^{9}$$

Steps Using Definition of a Derivative

Divide 20x^{8} by 4 to get 5x^{8}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{8}x^{2})$$

To multiply powers of the same base, add their exponents. Add 8 and 2 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{10})$$

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

$$10\times 5x^{10-1}$$

Multiply 10 times 5.

$$50x^{10-1}$$

Subtract 1 from 10.

$$50x^{9}$$