Solve -15y^9div5y^4

$$- 15 y ^ { 9 } \div 5 y ^ { 4 }$$

Evaluate

$$-3y^{13}$$

Solution Steps

Divide -15y^{9} by 5 to get -3y^{9}.

$$-3y^{9}y^{4}$$

To multiply powers of the same base, add their exponents. Add 9 and 4 to get 13.

$$-3y^{13}$$

Differentiate w.r.t. y

$$-39y^{12}$$

Steps Using Definition of a Derivative

Divide -15y^{9} by 5 to get -3y^{9}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-3y^{9}y^{4})$$

To multiply powers of the same base, add their exponents. Add 9 and 4 to get 13.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-3y^{13})$$

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

$$13\left(-3\right)y^{13-1}$$

Multiply 13 times -3.

$$-39y^{13-1}$$

Subtract 1 from 13.

$$-39y^{12}$$