Solve (y+5)+(2y+4y^2-2)

$$( y + 5 ) + ( 2 y + 4 y ^ { 2 } - 2 )$$

Evaluate

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

Solution Steps

Combine y and 2y to get 3y.

$$3y+5+4y^{2}-2$$

Subtract 2 from 5 to get 3.

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

Differentiate w.r.t. y

$$8y+3$$

Steps Using Derivative Rule for Sum

Combine y and 2y to get 3y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(3y+5+4y^{2}-2)$$

Subtract 2 from 5 to get 3.

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

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}.

$$3y^{1-1}+2\times 4y^{2-1}$$

Subtract 1 from 1.

$$3y^{0}+2\times 4y^{2-1}$$

Multiply 2 times 4.

$$3y^{0}+8y^{2-1}$$

Subtract 1 from 2.

$$3y^{0}+8y^{1}$$

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

$$3y^{0}+8y$$

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

$$3\times 1+8y$$

For any term t, t\times 1=t and 1t=t.

$$3+8y$$