Solve (4-8n^3+(7n^3-7)

$$( 4 - 8 n ^ { 3 } + ( 7 n ^ { 3 } - 7 )$$

Evaluate

$$-n^{3}-3$$

Solution Steps

Combine -8n^{3} and 7n^{3} to get -n^{3}.

$$4-n^{3}-7$$

Subtract 7 from 4 to get -3.

$$-3-n^{3}$$

Differentiate w.r.t. n

$$-3n^{2}$$

Steps Using Derivative Rule for Sum

Combine -8n^{3} and 7n^{3} to get -n^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}n}(4-n^{3}-7)$$

Subtract 7 from 4 to get -3.

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

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}.

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

Multiply 3 times -1.

$$-3n^{3-1}$$

Subtract 1 from 3.

$$-3n^{2}$$