Solve -5y^3+y^3-9y^3

$$- 5 y ^ { 3 } + y ^ { 3 } - 9 y ^ { 3 }$$

Evaluate

$$-13y^{3}$$

Solution Steps

Combine -5y^{3} and y^{3} to get -4y^{3}.

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

Combine -4y^{3} and -9y^{3} to get -13y^{3}.

$$-13y^{3}$$

Differentiate w.r.t. y

$$-39y^{2}$$

Steps Using Definition of a Derivative

Combine -5y^{3} and y^{3} to get -4y^{3}.

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

Combine -4y^{3} and -9y^{3} to get -13y^{3}.

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

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

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

Multiply 3 times -13.

$$-39y^{3-1}$$

Subtract 1 from 3.

$$-39y^{2}$$