Solve (4+2y^3-10y^2-8y+3)

$$( 4 + 2 y ^ { 3 } - 10 y ^ { 2 } - 8 y + 3 )$$

Differentiate w.r.t. y

$$6y^{2}-20y-8$$

Steps Using Derivative Rule for Sum

Add 4 and 3 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}y}(7+2y^{3}-10y^{2}-8y)$$

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}.

$$3\times 2y^{3-1}+2\left(-10\right)y^{2-1}-8y^{1-1}$$

Multiply 3 times 2.

$$6y^{3-1}+2\left(-10\right)y^{2-1}-8y^{1-1}$$

Subtract 1 from 3.

$$6y^{2}+2\left(-10\right)y^{2-1}-8y^{1-1}$$

Multiply 2 times -10.

$$6y^{2}-20y^{2-1}-8y^{1-1}$$

Subtract 1 from 2.

$$6y^{2}-20y^{1}-8y^{1-1}$$

Subtract 1 from 1.

$$6y^{2}-20y^{1}-8y^{0}$$

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

$$6y^{2}-20y-8y^{0}$$

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

$$6y^{2}-20y-8$$

Evaluate

$$2y^{3}-10y^{2}-8y+7$$

Solution Steps

Add 4 and 3 to get 7.

$$7+2y^{3}-10y^{2}-8y$$