Solve -7x^2+18x^2+3x^2-5x^2

$$- 7 x ^ { 2 } + 18 x ^ { 2 } + 3 x ^ { 2 } - 5 x ^ { 2 }$$

Evaluate

$$9x^{2}$$

Solution Steps

Combine -7x^{2} and 18x^{2} to get 11x^{2}.

$$11x^{2}+3x^{2}-5x^{2}$$

Combine 11x^{2} and 3x^{2} to get 14x^{2}.

$$14x^{2}-5x^{2}$$

Combine 14x^{2} and -5x^{2} to get 9x^{2}.

$$9x^{2}$$

Differentiate w.r.t. x

$$18x$$

Steps Using Definition of a Derivative

Combine -7x^{2} and 18x^{2} to get 11x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(11x^{2}+3x^{2}-5x^{2})$$

Combine 11x^{2} and 3x^{2} to get 14x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(14x^{2}-5x^{2})$$

Combine 14x^{2} and -5x^{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.

$$18x$$