Solve 15r^4*24r^10/6r^8=

$$\frac { 15 r ^ { 4 } \times 24 r ^ { 10 } } { 6 r ^ { 8 } } =$$

Evaluate

$$60r^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 10 to get 14.

$$\frac{15r^{14}\times 24}{6r^{8}}$$

Cancel out 2\times 3r^{8} in both numerator and denominator.

$$5\times 12r^{6}$$

Multiply 5 and 12 to get 60.

$$60r^{6}$$

Differentiate w.r.t. r

$$360r^{5}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{360r^{10}}{6}r^{4-8})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}r}(60r^{10}r^{-4})$$

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}.

$$-4\times 60r^{10}r^{-4-1}$$

Do the arithmetic.

$$\left(-240r^{10}\right)r^{-5}$$