Solve d/dx(3x^2+4x^2+7x+108)=

$$\frac { d } { d x } ( 3 x ^ { 2 } + 4 x ^ { 2 } + 7 x + 108 ) =$$

Evaluate

$$14x+7$$

Steps Using Derivative Rule for Sum

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{2}+7x+108)$$

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}.

$$2\times 7x^{2-1}+7x^{1-1}$$

Multiply 2 times 7.

$$14x^{2-1}+7x^{1-1}$$

Subtract 1 from 2.

$$14x^{1}+7x^{1-1}$$

Subtract 1 from 1.

$$14x^{1}+7x^{0}$$

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

$$14x+7x^{0}$$

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

$$14x+7\times 1$$

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

$$14x+7$$

Differentiate w.r.t. x

$$14$$