Solve (x^2+2)+(4x^2-5)

$$( x ^ { 2 } + 2 ) + ( 4 x ^ { 2 } - 5 )$$

Evaluate

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

Solution Steps

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

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

Subtract 5 from 2 to get -3.

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

Differentiate w.r.t. x

$$10x$$

Steps Using Derivative Rule for Sum

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

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

Subtract 5 from 2 to get -3.

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

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$2\times 5x^{2-1}$$

Multiply 2 times 5.

$$10x^{2-1}$$

Subtract 1 from 2.

$$10x^{1}$$

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

$$10x$$