Solve 102/100x+30/100(102/100x)

$$\frac { 102 } { 100 } x + \frac { 30 } { 100 } ( \frac { 102 } { 100 } x )$$

Evaluate

$$\frac{663x}{500}$$

Solution Steps

Reduce the fraction \frac{102}{100} to lowest terms by extracting and canceling out 2.

$$\frac{51}{50}x+\frac{30}{100}\times \frac{102}{100}x$$

Reduce the fraction \frac{30}{100} to lowest terms by extracting and canceling out 10.

$$\frac{51}{50}x+\frac{3}{10}\times \frac{102}{100}x$$

Reduce the fraction \frac{102}{100} to lowest terms by extracting and canceling out 2.

$$\frac{51}{50}x+\frac{3}{10}\times \frac{51}{50}x$$

Multiply \frac{3}{10} times \frac{51}{50} by multiplying numerator times numerator and denominator times denominator.

$$\frac{51}{50}x+\frac{3\times 51}{10\times 50}x$$

Do the multiplications in the fraction \frac{3\times 51}{10\times 50}.

$$\frac{51}{50}x+\frac{153}{500}x$$

Combine \frac{51}{50}x and \frac{153}{500}x to get \frac{663}{500}x.

$$\frac{663}{500}x$$

Differentiate w.r.t. x

$$\frac{663}{500} = 1\frac{163}{500} = 1.326$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{102}{100} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{51}{50}x+\frac{30}{100}\times \frac{102}{100}x)$$

Reduce the fraction \frac{30}{100} to lowest terms by extracting and canceling out 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{51}{50}x+\frac{3}{10}\times \frac{102}{100}x)$$

Reduce the fraction \frac{102}{100} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{51}{50}x+\frac{3}{10}\times \frac{51}{50}x)$$

Multiply \frac{3}{10} times \frac{51}{50} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{51}{50}x+\frac{3\times 51}{10\times 50}x)$$

Do the multiplications in the fraction \frac{3\times 51}{10\times 50}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{51}{50}x+\frac{153}{500}x)$$

Combine \frac{51}{50}x and \frac{153}{500}x to get \frac{663}{500}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{663}{500}x)$$

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

$$\frac{663}{500}x^{1-1}$$

Subtract 1 from 1.

$$\frac{663}{500}x^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{663}{500}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{663}{500}$$