Solve 20^2x^div5x^2=

$${ 20 }^{ 2 } { x }^{ } \div 5 { x }^{ 2 } =$$

Evaluate

$$80x^{3}$$

Solution Steps

Calculate 20 to the power of 2 and get 400.

$$\frac{400x^{1}}{5}x^{2}$$

Calculate x to the power of 1 and get x.

$$\frac{400x}{5}x^{2}$$

Divide 400x by 5 to get 80x.

$$80xx^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$80x^{3}$$

Differentiate w.r.t. x

$$240x^{2}$$

Steps Using Definition of a Derivative

Calculate 20 to the power of 2 and get 400.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{400x^{1}}{5}x^{2})$$

Calculate x to the power of 1 and get x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{400x}{5}x^{2})$$

Divide 400x by 5 to get 80x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(80xx^{2})$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(80x^{3})$$

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

$$3\times 80x^{3-1}$$

Multiply 3 times 80.

$$240x^{3-1}$$

Subtract 1 from 3.

$$240x^{2}$$