Solve 4x^2+3x^2+7x^2

$$4 { x }^{ 2 } +3 { x }^{ 2 } +7 { x }^{ 2 }$$

Evaluate

$$14x^{2}$$

Solution Steps

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

$$7x^{2}+7x^{2}$$

Combine 7x^{2} and 7x^{2} to get 14x^{2}.

$$14x^{2}$$

Differentiate w.r.t. x

$$28x$$

Steps Using Definition of a Derivative

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

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

Combine 7x^{2} and 7x^{2} to get 14x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(14x^{2})$$

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

$$2\times 14x^{2-1}$$

Multiply 2 times 14.

$$28x^{2-1}$$

Subtract 1 from 2.

$$28x^{1}$$

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

$$28x$$