Solve -12g+6g-5g^2-10+4g^2

$$- 12 g + 6 g - 5 g ^ { 2 } - 10 + 4 g ^ { 2 }$$

Evaluate

$$-g^{2}-6g-10$$

Solution Steps

Combine -12g and 6g to get -6g.

$$-6g-5g^{2}-10+4g^{2}$$

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

$$-6g-g^{2}-10$$

Differentiate w.r.t. g

$$-2g-6$$

Steps Using Derivative Rule for Sum

Combine -12g and 6g to get -6g.

$$\frac{\mathrm{d}}{\mathrm{d}g}(-6g-5g^{2}-10+4g^{2})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}g}(-6g-g^{2}-10)$$

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}.

$$-6g^{1-1}+2\left(-1\right)g^{2-1}$$

Subtract 1 from 1.

$$-6g^{0}+2\left(-1\right)g^{2-1}$$

Multiply 2 times -1.

$$-6g^{0}-2g^{2-1}$$

Subtract 1 from 2.

$$-6g^{0}-2g^{1}$$

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

$$-6g^{0}-2g$$

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

$$-6-2g$$