Solve 3x^2-2x^2+4x-x^2+x

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

Evaluate

$$5x$$

Solution Steps

Combine 3x^{2} and -2x^{2} to get x^{2}.

$$x^{2}+4x-x^{2}+x$$

Combine x^{2} and -x^{2} to get 0.

$$4x+x$$

Combine 4x and x to get 5x.

$$5x$$

Differentiate w.r.t. x

$$5$$

Steps Using Definition of a Derivative

Combine 3x^{2} and -2x^{2} to get x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}+4x-x^{2}+x)$$

Combine x^{2} and -x^{2} to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x+x)$$

Combine 4x and x to get 5x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x)$$

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

$$5x^{1-1}$$

Subtract 1 from 1.

$$5x^{0}$$

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

$$5\times 1$$

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

$$5$$