Solve (-8d^3-7)+(-d^3-6)

$$( - 8 d ^ { 3 } - 7 ) + ( - d ^ { 3 } - 6 )$$

Evaluate

$$-9d^{3}-13$$

Solution Steps

Subtract 6 from -7 to get -13.

$$-8d^{3}-13-d^{3}$$

Combine -8d^{3} and -d^{3} to get -9d^{3}.

$$-9d^{3}-13$$

Differentiate w.r.t. d

$$-27d^{2}$$

Steps Using Derivative Rule for Sum

Subtract 6 from -7 to get -13.

$$\frac{\mathrm{d}}{\mathrm{d}d}(-8d^{3}-13-d^{3})$$

Combine -8d^{3} and -d^{3} to get -9d^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}d}(-9d^{3}-13)$$

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}.

$$3\left(-9\right)d^{3-1}$$

Multiply 3 times -9.

$$-27d^{3-1}$$

Subtract 1 from 3.

$$-27d^{2}$$