Solve m^7div(-m^4divm)

$$m ^ { 7 } \div ( - m ^ { 4 } \div m )$$

Differentiate w.r.t. m

$$-4m^{3}$$

Steps Using Definition of a Derivative

Divide m^{7} by \frac{-m^{4}}{m} by multiplying m^{7} by the reciprocal of \frac{-m^{4}}{m}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{m^{7}m}{-m^{4}})$$

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{m^{8}}{-m^{4}})$$

Cancel out m^{4} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{m^{4}}{-1})$$

Anything divided by -1 gives its opposite.

$$\frac{\mathrm{d}}{\mathrm{d}m}(-m^{4})$$

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

$$4\left(-1\right)m^{4-1}$$

Multiply 4 times -1.

$$-4m^{4-1}$$

Subtract 1 from 4.

$$-4m^{3}$$

Evaluate

$$-m^{4}$$