Solve (-5d+3)+(-6d^3-d^2+2d+6)

$$( - 5 d + 3 ) + ( - 6 d ^ { 3 } - d ^ { 2 } + 2 d + 6 )$$

Evaluate

$$9-3d-d^{2}-6d^{3}$$

Solution Steps

Combine -5d and 2d to get -3d.

$$-3d+3-6d^{3}-d^{2}+6$$

Add 3 and 6 to get 9.

$$-3d+9-6d^{3}-d^{2}$$

Differentiate w.r.t. d

$$-18d^{2}-2d-3$$

Steps Using Derivative Rule for Sum

Combine -5d and 2d to get -3d.

$$\frac{\mathrm{d}}{\mathrm{d}d}(-3d+3-6d^{3}-d^{2}+6)$$

Add 3 and 6 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}d}(-3d+9-6d^{3}-d^{2})$$

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}.

$$-3d^{1-1}+3\left(-6\right)d^{3-1}+2\left(-1\right)d^{2-1}$$

Subtract 1 from 1.

$$-3d^{0}+3\left(-6\right)d^{3-1}+2\left(-1\right)d^{2-1}$$

Multiply 3 times -6.

$$-3d^{0}-18d^{3-1}+2\left(-1\right)d^{2-1}$$

Subtract 1 from 3.

$$-3d^{0}-18d^{2}+2\left(-1\right)d^{2-1}$$

Multiply 3 times -6.

$$-3d^{0}-18d^{2}-2d^{2-1}$$

Subtract 1 from 2.

$$-3d^{0}-18d^{2}-2d^{1}$$

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

$$-3d^{0}-18d^{2}-2d$$

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

$$-3-18d^{2}-2d$$