Solve r^4/r^-2

$$\frac { r ^ { 4 } } { r ^ { - 2 } }$$

Differentiate w.r.t. r

$$6r^{5}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{1}{1}r^{4-\left(-2\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}r}(r^{6})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$6r^{6-1}$$

Do the arithmetic.

$$6r^{5}$$

Evaluate

$$r^{6}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -2 from 4 to get 6.

$$r^{6}$$