Solve d(4Q^3-30Q^2+90Q+60)/dQ

$$\frac { d ( 4 Q ^ { 3 } - 30 Q ^ { 2 } + 90 Q + 60 ) } { d Q }$$

Evaluate

$$12Q^{2}-60Q+90$$

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}.

$$3\times 4Q^{3-1}+2\left(-30\right)Q^{2-1}+90Q^{1-1}$$

Multiply 3 times 4.

$$12Q^{3-1}+2\left(-30\right)Q^{2-1}+90Q^{1-1}$$

Subtract 1 from 3.

$$12Q^{2}+2\left(-30\right)Q^{2-1}+90Q^{1-1}$$

Multiply 2 times -30.

$$12Q^{2}-60Q^{2-1}+90Q^{1-1}$$

Subtract 1 from 2.

$$12Q^{2}-60Q^{1}+90Q^{1-1}$$

Subtract 1 from 1.

$$12Q^{2}-60Q^{1}+90Q^{0}$$

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

$$12Q^{2}-60Q+90Q^{0}$$

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

$$12Q^{2}-60Q+90\times 1$$

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

$$12Q^{2}-60Q+90$$

Differentiate w.r.t. Q

$$24Q-60$$