Solve 2x^2+5x-9-4x^2

$$2 x ^ { 2 } + 5 x - 9 - 4 x ^ { 2 }$$

Differentiate w.r.t. x

$$5-4x$$

Steps Using Derivative Rule for Sum

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x^{2}+5x-9)$$

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}.

$$2\left(-2\right)x^{2-1}+5x^{1-1}$$

Multiply 2 times -2.

$$-4x^{2-1}+5x^{1-1}$$

Subtract 1 from 2.

$$-4x^{1}+5x^{1-1}$$

Subtract 1 from 1.

$$-4x^{1}+5x^{0}$$

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

$$-4x+5x^{0}$$

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

$$-4x+5\times 1$$

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

$$-4x+5$$

Evaluate

$$-2x^{2}+5x-9$$

Solution Steps

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

$$-2x^{2}+5x-9$$