Solve 2/5X(-3/7)-1/6X3/2+frac{1}{14}Xfrac{2}{5}

$$\frac { 2 } { 5 } X ( - \frac { 3 } { 7 } ) - \frac { 1 } { 6 } X \frac { 3 } { 2 } + \frac { 1 } { 14 } X \frac { 2 } { 5 }$$

Evaluate

$$-\frac{11X}{28}$$

Solution Steps

Multiply \frac{2}{5} times -\frac{3}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\left(-3\right)}{5\times 7}X-\frac{1}{6}X\times \frac{3}{2}+\frac{1}{14}X\times \frac{2}{5}$$

Do the multiplications in the fraction \frac{2\left(-3\right)}{5\times 7}.

$$\frac{-6}{35}X-\frac{1}{6}X\times \frac{3}{2}+\frac{1}{14}X\times \frac{2}{5}$$

Fraction \frac{-6}{35} can be rewritten as -\frac{6}{35} by extracting the negative sign.

$$-\frac{6}{35}X-\frac{1}{6}X\times \frac{3}{2}+\frac{1}{14}X\times \frac{2}{5}$$

Multiply \frac{1}{6} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{6}{35}X-\frac{1\times 3}{6\times 2}X+\frac{1}{14}X\times \frac{2}{5}$$

Do the multiplications in the fraction \frac{1\times 3}{6\times 2}.

$$-\frac{6}{35}X-\frac{3}{12}X+\frac{1}{14}X\times \frac{2}{5}$$

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

$$-\frac{6}{35}X-\frac{1}{4}X+\frac{1}{14}X\times \frac{2}{5}$$

Combine -\frac{6}{35}X and -\frac{1}{4}X to get -\frac{59}{140}X.

$$-\frac{59}{140}X+\frac{1}{14}X\times \frac{2}{5}$$

Multiply \frac{1}{14} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{59}{140}X+\frac{1\times 2}{14\times 5}X$$

Do the multiplications in the fraction \frac{1\times 2}{14\times 5}.

$$-\frac{59}{140}X+\frac{2}{70}X$$

Reduce the fraction \frac{2}{70} to lowest terms by extracting and canceling out 2.

$$-\frac{59}{140}X+\frac{1}{35}X$$

Combine -\frac{59}{140}X and \frac{1}{35}X to get -\frac{11}{28}X.

$$-\frac{11}{28}X$$

Differentiate w.r.t. X

$$-\frac{11}{28} = -0.39285714285714285$$

Steps Using Definition of a Derivative

Multiply \frac{2}{5} times -\frac{3}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}X}(\frac{2\left(-3\right)}{5\times 7}X-\frac{1}{6}X\times \frac{3}{2}+\frac{1}{14}X\times \frac{2}{5})$$

Do the multiplications in the fraction \frac{2\left(-3\right)}{5\times 7}.

$$\frac{\mathrm{d}}{\mathrm{d}X}(\frac{-6}{35}X-\frac{1}{6}X\times \frac{3}{2}+\frac{1}{14}X\times \frac{2}{5})$$

Fraction \frac{-6}{35} can be rewritten as -\frac{6}{35} by extracting the negative sign.

$$\frac{\mathrm{d}}{\mathrm{d}X}(-\frac{6}{35}X-\frac{1}{6}X\times \frac{3}{2}+\frac{1}{14}X\times \frac{2}{5})$$

Multiply \frac{1}{6} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}X}(-\frac{6}{35}X-\frac{1\times 3}{6\times 2}X+\frac{1}{14}X\times \frac{2}{5})$$

Do the multiplications in the fraction \frac{1\times 3}{6\times 2}.

$$\frac{\mathrm{d}}{\mathrm{d}X}(-\frac{6}{35}X-\frac{3}{12}X+\frac{1}{14}X\times \frac{2}{5})$$

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

$$\frac{\mathrm{d}}{\mathrm{d}X}(-\frac{6}{35}X-\frac{1}{4}X+\frac{1}{14}X\times \frac{2}{5})$$

Combine -\frac{6}{35}X and -\frac{1}{4}X to get -\frac{59}{140}X.

$$\frac{\mathrm{d}}{\mathrm{d}X}(-\frac{59}{140}X+\frac{1}{14}X\times \frac{2}{5})$$

Multiply \frac{1}{14} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}X}(-\frac{59}{140}X+\frac{1\times 2}{14\times 5}X)$$

Do the multiplications in the fraction \frac{1\times 2}{14\times 5}.

$$\frac{\mathrm{d}}{\mathrm{d}X}(-\frac{59}{140}X+\frac{2}{70}X)$$

Reduce the fraction \frac{2}{70} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}X}(-\frac{59}{140}X+\frac{1}{35}X)$$

Combine -\frac{59}{140}X and \frac{1}{35}X to get -\frac{11}{28}X.

$$\frac{\mathrm{d}}{\mathrm{d}X}(-\frac{11}{28}X)$$

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

$$-\frac{11}{28}X^{1-1}$$

Subtract 1 from 1.

$$-\frac{11}{28}X^{0}$$

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

$$-\frac{11}{28}$$