Solve 952m^2quad12m/quad544.5m^2

$$952 m ^ { 2 } \quad 12 m / \quad 544.5 m ^ { 2 }$$

Evaluate

$$\frac{7616m^{5}}{363}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{952m^{3}\times 12}{544.5}m^{2}$$

Multiply 952 and 12 to get 11424.

$$\frac{11424m^{3}}{544.5}m^{2}$$

Divide 11424m^{3} by 544.5 to get \frac{7616}{363}m^{3}.

$$\frac{7616}{363}m^{3}m^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{7616}{363}m^{5}$$

Differentiate w.r.t. m

$$\frac{38080m^{4}}{363}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{952m^{3}\times 12}{544.5}m^{2})$$

Multiply 952 and 12 to get 11424.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{11424m^{3}}{544.5}m^{2})$$

Divide 11424m^{3} by 544.5 to get \frac{7616}{363}m^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{7616}{363}m^{3}m^{2})$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{7616}{363}m^{5})$$

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

$$5\times \frac{7616}{363}m^{5-1}$$

Multiply 5 times \frac{7616}{363}.

$$\frac{38080}{363}m^{5-1}$$

Subtract 1 from 5.

$$\frac{38080}{363}m^{4}$$