Solve {l}{2x^2+4x^2}{+3x^2}

$$\left. \begin{array} { l } { 2 x ^ { 2 } + 4 x ^ { 2 } } \\ { + 3 x ^ { 2 } } \end{array} \right.$$

Evaluate

$$9x^{2}$$

Solution Steps

Combine 2x^{2} and 4x^{2} to get 6x^{2}.

$$6x^{2}+3x^{2}$$

Combine 6x^{2} and 3x^{2} to get 9x^{2}.

$$9x^{2}$$

Differentiate w.r.t. x

$$18x$$

Steps Using Definition of a Derivative

Combine 2x^{2} and 4x^{2} to get 6x^{2}.

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

Combine 6x^{2} and 3x^{2} to get 9x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x^{2})$$

The derivative of ax^{n} is nax^{n-1}.

$$2\times 9x^{2-1}$$

Multiply 2 times 9.

$$18x^{2-1}$$

Subtract 1 from 2.

$$18x^{1}$$

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

$$18x$$