Solve 3y*y+4y^2

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

Evaluate

$$7y^{2}$$

Solution Steps

Multiply y and y to get y^{2}.

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

Combine 3y^{2} and 4y^{2} to get 7y^{2}.

$$7y^{2}$$

Differentiate w.r.t. y

$$14y$$

Steps Using Derivative Rule for Sum

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}.

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

Subtract 1 from 1.

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

Multiply 2 times 4.

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

Subtract 1 from 2.

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

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

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

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

$$3y\times 1+8y$$

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

$$3y+8y$$