Solve -8x^5div12x^9

$$- 8 x ^ { 5 } \div 12 x ^ { 9 }$$

Evaluate

$$-\frac{2x^{14}}{3}$$

Solution Steps

Divide -8x^{5} by 12 to get -\frac{2}{3}x^{5}.

$$-\frac{2}{3}x^{5}x^{9}$$

To multiply powers of the same base, add their exponents. Add 5 and 9 to get 14.

$$-\frac{2}{3}x^{14}$$

Differentiate w.r.t. x

$$-\frac{28x^{13}}{3}$$

Steps Using Definition of a Derivative

Divide -8x^{5} by 12 to get -\frac{2}{3}x^{5}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{2}{3}x^{5}x^{9})$$

To multiply powers of the same base, add their exponents. Add 5 and 9 to get 14.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{2}{3}x^{14})$$

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

$$14\left(-\frac{2}{3}\right)x^{14-1}$$

Multiply 14 times -\frac{2}{3}.

$$-\frac{28}{3}x^{14-1}$$

Subtract 1 from 14.

$$-\frac{28}{3}x^{13}$$