Solve g*(12/5*7/4)div3/2

$$g \cdot ( \frac { 12 } { 5 } \cdot \frac { 7 } { 4 } ) \div \frac { 3 } { 2 }$$

Evaluate

$$\frac{14g}{5}$$

Solution Steps

Multiply \frac{12}{5} times \frac{7}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{g\times \frac{12\times 7}{5\times 4}}{\frac{3}{2}}$$

Do the multiplications in the fraction \frac{12\times 7}{5\times 4}.

$$\frac{g\times \frac{84}{20}}{\frac{3}{2}}$$

Reduce the fraction \frac{84}{20} to lowest terms by extracting and canceling out 4.

$$\frac{g\times \frac{21}{5}}{\frac{3}{2}}$$

Divide g\times \frac{21}{5} by \frac{3}{2} by multiplying g\times \frac{21}{5} by the reciprocal of \frac{3}{2}.

$$\frac{g\times \frac{21}{5}\times 2}{3}$$

Express \frac{21}{5}\times 2 as a single fraction.

$$\frac{g\times \frac{21\times 2}{5}}{3}$$

Multiply 21 and 2 to get 42.

$$\frac{g\times \frac{42}{5}}{3}$$

Divide g\times \frac{42}{5} by 3 to get g\times \frac{14}{5}.

$$g\times \frac{14}{5}$$

Differentiate w.r.t. g

$$\frac{14}{5} = 2\frac{4}{5} = 2.8$$

Steps Using Definition of a Derivative

Multiply \frac{12}{5} times \frac{7}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{g\times \frac{12\times 7}{5\times 4}}{\frac{3}{2}})$$

Do the multiplications in the fraction \frac{12\times 7}{5\times 4}.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{g\times \frac{84}{20}}{\frac{3}{2}})$$

Reduce the fraction \frac{84}{20} to lowest terms by extracting and canceling out 4.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{g\times \frac{21}{5}}{\frac{3}{2}})$$

Divide g\times \frac{21}{5} by \frac{3}{2} by multiplying g\times \frac{21}{5} by the reciprocal of \frac{3}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{g\times \frac{21}{5}\times 2}{3})$$

Express \frac{21}{5}\times 2 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{g\times \frac{21\times 2}{5}}{3})$$

Multiply 21 and 2 to get 42.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{g\times \frac{42}{5}}{3})$$

Divide g\times \frac{42}{5} by 3 to get g\times \frac{14}{5}.

$$\frac{\mathrm{d}}{\mathrm{d}g}(g\times \frac{14}{5})$$

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

$$\frac{14}{5}g^{1-1}$$

Subtract 1 from 1.

$$\frac{14}{5}g^{0}$$

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

$$\frac{14}{5}\times 1$$

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

$$\frac{14}{5}$$