Solve frac{21m^frac{3{2}}}{1/3}

$$\frac { 21 m ^ { \frac { 3 } { 2 } } } { \frac { 1 } { 3 } }$$

Evaluate

$$63m^{\frac{3}{2}}$$

Solution Steps

Divide 21m^{\frac{3}{2}} by \frac{1}{3} by multiplying 21m^{\frac{3}{2}} by the reciprocal of \frac{1}{3}.

$$21m^{\frac{3}{2}}\times 3$$

Multiply 21 and 3 to get 63.

$$63m^{\frac{3}{2}}$$

Differentiate w.r.t. m

$$\frac{189\sqrt{m}}{2}$$

Steps Using Definition of a Derivative

Divide 21m^{\frac{3}{2}} by \frac{1}{3} by multiplying 21m^{\frac{3}{2}} by the reciprocal of \frac{1}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(21m^{\frac{3}{2}}\times 3)$$

Multiply 21 and 3 to get 63.

$$\frac{\mathrm{d}}{\mathrm{d}m}(63m^{\frac{3}{2}})$$

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

$$\frac{3}{2}\times 63m^{\frac{3}{2}-1}$$

Multiply \frac{3}{2} times 63.

$$\frac{189}{2}m^{\frac{3}{2}-1}$$

Subtract 1 from \frac{3}{2}.

$$\frac{189}{2}\sqrt{m}$$