Solve (2n^5+2-11n^3)+(-6-n^5+9n^3)

$$( 2 n ^ { 5 } + 2 - 11 n ^ { 3 } ) + ( - 6 - n ^ { 5 } + 9 n ^ { 3 } )$$

Evaluate

$$n^{5}-2n^{3}-4$$

Solution Steps

Subtract 6 from 2 to get -4.

$$2n^{5}-4-11n^{3}-n^{5}+9n^{3}$$

Combine 2n^{5} and -n^{5} to get n^{5}.

$$n^{5}-4-11n^{3}+9n^{3}$$

Combine -11n^{3} and 9n^{3} to get -2n^{3}.

$$n^{5}-4-2n^{3}$$

Differentiate w.r.t. n

$$n^{2}\left(5n^{2}-6\right)$$

Steps Using Derivative Rule for Sum

Subtract 6 from 2 to get -4.

$$\frac{\mathrm{d}}{\mathrm{d}n}(2n^{5}-4-11n^{3}-n^{5}+9n^{3})$$

Combine 2n^{5} and -n^{5} to get n^{5}.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n^{5}-4-11n^{3}+9n^{3})$$

Combine -11n^{3} and 9n^{3} to get -2n^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n^{5}-4-2n^{3})$$

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}.

$$5n^{5-1}+3\left(-2\right)n^{3-1}$$

Subtract 1 from 5.

$$5n^{4}+3\left(-2\right)n^{3-1}$$

Multiply 3 times -2.

$$5n^{4}-6n^{3-1}$$

Subtract 1 from 3.

$$5n^{4}-6n^{2}$$