Solve 2y^3+5y^2-8y-622y+1

$$2 y ^ { 3 } + 5 y ^ { 2 } - 8 y - 622 y + 1$$

Differentiate w.r.t. y

$$6y^{2}+10y-630$$

Steps Using Derivative Rule for Sum

Combine -8y and -622y to get -630y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(2y^{3}+5y^{2}-630y+1)$$

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}.

$$3\times 2y^{3-1}+2\times 5y^{2-1}-630y^{1-1}$$

Multiply 3 times 2.

$$6y^{3-1}+2\times 5y^{2-1}-630y^{1-1}$$

Subtract 1 from 3.

$$6y^{2}+2\times 5y^{2-1}-630y^{1-1}$$

Multiply 2 times 5.

$$6y^{2}+10y^{2-1}-630y^{1-1}$$

Subtract 1 from 2.

$$6y^{2}+10y^{1}-630y^{1-1}$$

Subtract 1 from 1.

$$6y^{2}+10y^{1}-630y^{0}$$

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

$$6y^{2}+10y-630y^{0}$$

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

$$6y^{2}+10y-630$$

Evaluate

$$2y^{3}+5y^{2}-630y+1$$

Solution Steps

Combine -8y and -622y to get -630y.

$$2y^{3}+5y^{2}-630y+1$$