Solve 3x^2%3*2=

$$3 { x }^{ 2 } \% 3 \times 2=$$

Evaluate

$$\frac{9x^{2}}{50}$$

Solution Steps

Multiply 3 and 3 to get 9.

$$9\times \frac{x^{2}}{100}\times 2$$

Multiply 9 and 2 to get 18.

$$18\times \frac{x^{2}}{100}$$

Express 18\times \frac{x^{2}}{100} as a single fraction.

$$\frac{18x^{2}}{100}$$

Divide 18x^{2} by 100 to get \frac{9}{50}x^{2}.

$$\frac{9}{50}x^{2}$$

Differentiate w.r.t. x

$$\frac{9x}{25}$$

Steps Using Definition of a Derivative

Multiply 3 and 3 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9\times \frac{x^{2}}{100}\times 2)$$

Multiply 9 and 2 to get 18.

$$\frac{\mathrm{d}}{\mathrm{d}x}(18\times \frac{x^{2}}{100})$$

Express 18\times \frac{x^{2}}{100} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{18x^{2}}{100})$$

Divide 18x^{2} by 100 to get \frac{9}{50}x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{9}{50}x^{2})$$

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

$$2\times \frac{9}{50}x^{2-1}$$

Multiply 2 times \frac{9}{50}.

$$\frac{9}{25}x^{2-1}$$

Subtract 1 from 2.

$$\frac{9}{25}x^{1}$$

For any term t, t^{1}=t.

$$\frac{9}{25}x$$