Solve 4x^2+5x^2-3x^2=

$$4 x ^ { 2 } + 5 x ^ { 2 } - 3 x ^ { 2 } =$$

Evaluate

$$6x^{2}$$

Solution Steps

Combine 4x^{2} and 5x^{2} to get 9x^{2}.

$$9x^{2}-3x^{2}$$

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

$$6x^{2}$$

Differentiate w.r.t. x

$$12x$$

Steps Using Definition of a Derivative

Combine 4x^{2} and 5x^{2} to get 9x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x^{2}-3x^{2})$$

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

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

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

$$2\times 6x^{2-1}$$

Multiply 2 times 6.

$$12x^{2-1}$$

Subtract 1 from 2.

$$12x^{1}$$

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

$$12x$$