Solve 15y^2+7y-9y^2-4y+5=

$$15 y ^ { 2 } + 7 y - 9 y ^ { 2 } - 4 y + 5 =$$

Evaluate

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

Solution Steps

Combine 15y^{2} and -9y^{2} to get 6y^{2}.

$$6y^{2}+7y-4y+5$$

Combine 7y and -4y to get 3y.

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

Differentiate w.r.t. y

$$12y+3$$

Steps Using Derivative Rule for Sum

Combine 15y^{2} and -9y^{2} to get 6y^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(6y^{2}+7y-4y+5)$$

Combine 7y and -4y to get 3y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(6y^{2}+3y+5)$$

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}.

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

Multiply 2 times 6.

$$12y^{2-1}+3y^{1-1}$$

Subtract 1 from 2.

$$12y^{1}+3y^{1-1}$$

Subtract 1 from 1.

$$12y^{1}+3y^{0}$$

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

$$12y+3y^{0}$$

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

$$12y+3\times 1$$

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

$$12y+3$$