Solve (3/7x-5/9)div(-5/12*12/49)

$$( \frac { 3 } { 7 } x \frac { - 5 } { 9 } ) \div ( - \frac { 5 } { 12 } \times \frac { 12 } { 49 } )$$

Evaluate

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

Solution Steps

Fraction \frac{-5}{9} can be rewritten as -\frac{5}{9} by extracting the negative sign.

$$\frac{\frac{3}{7}x\left(-\frac{5}{9}\right)}{-\frac{5}{12}\times \frac{12}{49}}$$

Multiply \frac{3}{7} times -\frac{5}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3\left(-5\right)}{7\times 9}x}{-\frac{5}{12}\times \frac{12}{49}}$$

Do the multiplications in the fraction \frac{3\left(-5\right)}{7\times 9}.

$$\frac{\frac{-15}{63}x}{-\frac{5}{12}\times \frac{12}{49}}$$

Reduce the fraction \frac{-15}{63} to lowest terms by extracting and canceling out 3.

$$\frac{-\frac{5}{21}x}{-\frac{5}{12}\times \frac{12}{49}}$$

Multiply -\frac{5}{12} times \frac{12}{49} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\frac{5}{21}x}{\frac{-5\times 12}{12\times 49}}$$

Cancel out 12 in both numerator and denominator.

$$\frac{-\frac{5}{21}x}{\frac{-5}{49}}$$

Fraction \frac{-5}{49} can be rewritten as -\frac{5}{49} by extracting the negative sign.

$$\frac{-\frac{5}{21}x}{-\frac{5}{49}}$$

Divide -\frac{5}{21}x by -\frac{5}{49} by multiplying -\frac{5}{21}x by the reciprocal of -\frac{5}{49}.

$$\frac{-\frac{5}{21}x\times 49}{-5}$$

Express -\frac{5}{21}\times 49 as a single fraction.

$$\frac{\frac{-5\times 49}{21}x}{-5}$$

Multiply -5 and 49 to get -245.

$$\frac{\frac{-245}{21}x}{-5}$$

Reduce the fraction \frac{-245}{21} to lowest terms by extracting and canceling out 7.

$$\frac{-\frac{35}{3}x}{-5}$$

Divide -\frac{35}{3}x by -5 to get \frac{7}{3}x.

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

Differentiate w.r.t. x

$$\frac{7}{3} = 2\frac{1}{3} = 2.3333333333333335$$

Steps Using Definition of a Derivative

Fraction \frac{-5}{9} can be rewritten as -\frac{5}{9} by extracting the negative sign.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{3}{7}x\left(-\frac{5}{9}\right)}{-\frac{5}{12}\times \frac{12}{49}})$$

Multiply \frac{3}{7} times -\frac{5}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{3\left(-5\right)}{7\times 9}x}{-\frac{5}{12}\times \frac{12}{49}})$$

Do the multiplications in the fraction \frac{3\left(-5\right)}{7\times 9}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{-15}{63}x}{-\frac{5}{12}\times \frac{12}{49}})$$

Reduce the fraction \frac{-15}{63} to lowest terms by extracting and canceling out 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-\frac{5}{21}x}{-\frac{5}{12}\times \frac{12}{49}})$$

Multiply -\frac{5}{12} times \frac{12}{49} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-\frac{5}{21}x}{\frac{-5\times 12}{12\times 49}})$$

Cancel out 12 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-\frac{5}{21}x}{\frac{-5}{49}})$$

Fraction \frac{-5}{49} can be rewritten as -\frac{5}{49} by extracting the negative sign.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-\frac{5}{21}x}{-\frac{5}{49}})$$

Divide -\frac{5}{21}x by -\frac{5}{49} by multiplying -\frac{5}{21}x by the reciprocal of -\frac{5}{49}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-\frac{5}{21}x\times 49}{-5})$$

Express -\frac{5}{21}\times 49 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{-5\times 49}{21}x}{-5})$$

Multiply -5 and 49 to get -245.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{-245}{21}x}{-5})$$

Reduce the fraction \frac{-245}{21} to lowest terms by extracting and canceling out 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-\frac{35}{3}x}{-5})$$

Divide -\frac{35}{3}x by -5 to get \frac{7}{3}x.

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

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

$$\frac{7}{3}x^{1-1}$$

Subtract 1 from 1.

$$\frac{7}{3}x^{0}$$

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

$$\frac{7}{3}\times 1$$

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

$$\frac{7}{3}$$