Solve 7x(6/12*4/6)5^2

$$7x( \frac{ 6 }{ 12 } \times \frac{ 4 }{ 6 } ) { 5 }^{ 2 }$$

Evaluate

$$\frac{175x}{3}$$

Solution Steps

Reduce the fraction \frac{6}{12} to lowest terms by extracting and canceling out 6.

$$7x\times \frac{1}{2}\times \frac{4}{6}\times 5^{2}$$

Multiply 7 and \frac{1}{2} to get \frac{7}{2}.

$$\frac{7}{2}x\times \frac{4}{6}\times 5^{2}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{7}{2}x\times \frac{2}{3}\times 5^{2}$$

Multiply \frac{7}{2} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 2}{2\times 3}x\times 5^{2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{7}{3}x\times 5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{7}{3}x\times 25$$

Express \frac{7}{3}\times 25 as a single fraction.

$$\frac{7\times 25}{3}x$$

Multiply 7 and 25 to get 175.

$$\frac{175}{3}x$$

Differentiate w.r.t. x

$$\frac{175}{3} = 58\frac{1}{3} = 58.333333333333336$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{6}{12} to lowest terms by extracting and canceling out 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x\times \frac{1}{2}\times \frac{4}{6}\times 5^{2})$$

Multiply 7 and \frac{1}{2} to get \frac{7}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7}{2}x\times \frac{4}{6}\times 5^{2})$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7}{2}x\times \frac{2}{3}\times 5^{2})$$

Multiply \frac{7}{2} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7\times 2}{2\times 3}x\times 5^{2})$$

Cancel out 2 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7}{3}x\times 5^{2})$$

Calculate 5 to the power of 2 and get 25.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7}{3}x\times 25)$$

Express \frac{7}{3}\times 25 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7\times 25}{3}x)$$

Multiply 7 and 25 to get 175.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{175}{3}x)$$

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

$$\frac{175}{3}x^{1-1}$$

Subtract 1 from 1.

$$\frac{175}{3}x^{0}$$

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

$$\frac{175}{3}\times 1$$

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

$$\frac{175}{3}$$