Solve 5/100X7/10

$$\frac { 5 } { 100 } X \frac { 7 } { 10 }$$

Evaluate

$$\frac{7X}{200}$$

Solution Steps

Reduce the fraction \frac{5}{100} to lowest terms by extracting and canceling out 5.

$$\frac{1}{20}X\times \frac{7}{10}$$

Multiply \frac{1}{20} times \frac{7}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 7}{20\times 10}X$$

Do the multiplications in the fraction \frac{1\times 7}{20\times 10}.

$$\frac{7}{200}X$$

Differentiate w.r.t. X

$$\frac{7}{200} = 0.035$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{5}{100} to lowest terms by extracting and canceling out 5.

$$\frac{\mathrm{d}}{\mathrm{d}X}(\frac{1}{20}X\times \frac{7}{10})$$

Multiply \frac{1}{20} times \frac{7}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}X}(\frac{1\times 7}{20\times 10}X)$$

Do the multiplications in the fraction \frac{1\times 7}{20\times 10}.

$$\frac{\mathrm{d}}{\mathrm{d}X}(\frac{7}{200}X)$$

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

$$\frac{7}{200}X^{1-1}$$

Subtract 1 from 1.

$$\frac{7}{200}X^{0}$$

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

$$\frac{7}{200}\times 1$$

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

$$\frac{7}{200}$$