Solve -36y^3div9y^2

$$- 36 y ^ { 3 } \div 9 y ^ { 2 }$$

Evaluate

$$-4y^{5}$$

Solution Steps

Divide -36y^{3} by 9 to get -4y^{3}.

$$-4y^{3}y^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$-4y^{5}$$

Differentiate w.r.t. y

$$-20y^{4}$$

Steps Using Definition of a Derivative

Divide -36y^{3} by 9 to get -4y^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-4y^{3}y^{2})$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-4y^{5})$$

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

$$5\left(-4\right)y^{5-1}$$

Multiply 5 times -4.

$$-20y^{5-1}$$

Subtract 1 from 5.

$$-20y^{4}$$