Solve 6+2y^3-5y^3-y

$$6 + 2 y ^ { 3 } - 5 y ^ { 3 } - y$$

Differentiate w.r.t. y

$$-9y^{2}-1$$

Steps Using Derivative Rule for Sum

Combine 2y^{3} and -5y^{3} to get -3y^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(6-3y^{3}-y)$$

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}.

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

Multiply 3 times -3.

$$-9y^{3-1}-y^{1-1}$$

Subtract 1 from 3.

$$-9y^{2}-y^{1-1}$$

Subtract 1 from 1.

$$-9y^{2}-y^{0}$$

For any term t except 0, t^{0}=1.

$$-9y^{2}-1$$

Evaluate

$$6-y-3y^{3}$$

Solution Steps

Combine 2y^{3} and -5y^{3} to get -3y^{3}.

$$6-3y^{3}-y$$