Solve (2x/2/5)*(7/63)

$$( \frac { \frac { 2 x } { 2 } } { 5 } ) \times ( \frac { 7 } { 63 } )$$

Evaluate

$$\frac{x}{45}$$

Solution Steps

Express \frac{\frac{2x}{2}}{5} as a single fraction.

$$\frac{2x}{2\times 5}\times \frac{7}{63}$$

Cancel out 2 in both numerator and denominator.

$$\frac{x}{5}\times \frac{7}{63}$$

Reduce the fraction \frac{7}{63} to lowest terms by extracting and canceling out 7.

$$\frac{x}{5}\times \frac{1}{9}$$

Multiply \frac{x}{5} times \frac{1}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x}{5\times 9}$$

Multiply 5 and 9 to get 45.

$$\frac{x}{45}$$

Differentiate w.r.t. x

$$\frac{1}{45} = 0.022222222222222223$$

Steps Using Definition of a Derivative

Express \frac{\frac{2x}{2}}{5} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x}{2\times 5}\times \frac{7}{63})$$

Cancel out 2 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{5}\times \frac{7}{63})$$

Reduce the fraction \frac{7}{63} to lowest terms by extracting and canceling out 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{5}\times \frac{1}{9})$$

Multiply \frac{x}{5} times \frac{1}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{5\times 9})$$

Multiply 5 and 9 to get 45.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{45})$$

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

$$\frac{1}{45}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{45}x^{0}$$

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

$$\frac{1}{45}\times 1$$

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

$$\frac{1}{45}$$