Solve (y^2-y+3)+(y+2)

$$( y ^ { 2 } - y + 3 ) + ( y + 2 )$$

Evaluate

$$y^{2}+5$$

Solution Steps

Combine -y and y to get 0.

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

Add 3 and 2 to get 5.

$$y^{2}+5$$

Differentiate w.r.t. y

$$2y$$

Steps Using Derivative Rule for Sum

Combine -y and y to get 0.

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

Add 3 and 2 to get 5.

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

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}.

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

Subtract 1 from 2.

$$2y^{1}$$

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

$$2y$$