Solve -9x^2+4x^2+-7x^2+-4x^2

$$-9 { x }^{ 2 } +4 { x }^{ 2 } +-7 { x }^{ 2 } +-4 { x }^{ 2 }$$

Evaluate

$$-16x^{2}$$

Solution Steps

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

$$-5x^{2}-7x^{2}-4x^{2}$$

Combine -5x^{2} and -7x^{2} to get -12x^{2}.

$$-12x^{2}-4x^{2}$$

Combine -12x^{2} and -4x^{2} to get -16x^{2}.

$$-16x^{2}$$

Differentiate w.r.t. x

$$-32x$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-5x^{2}-7x^{2}-4x^{2})$$

Combine -5x^{2} and -7x^{2} to get -12x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-12x^{2}-4x^{2})$$

Combine -12x^{2} and -4x^{2} to get -16x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-16x^{2})$$

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

$$2\left(-16\right)x^{2-1}$$

Multiply 2 times -16.

$$-32x^{2-1}$$

Subtract 1 from 2.

$$-32x^{1}$$

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

$$-32x$$