Solve k^4+6k^2+23k^2+42k+24

$$k ^ { 4 } + 6 k ^ { 2 } + 23 k ^ { 2 } + 42 k + 24$$

Differentiate w.r.t. k

$$4k^{3}+58k+42$$

Steps Using Derivative Rule for Sum

Combine 6k^{2} and 23k^{2} to get 29k^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}k}(k^{4}+29k^{2}+42k+24)$$

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}.

$$4k^{4-1}+2\times 29k^{2-1}+42k^{1-1}$$

Subtract 1 from 4.

$$4k^{3}+2\times 29k^{2-1}+42k^{1-1}$$

Multiply 2 times 29.

$$4k^{3}+58k^{2-1}+42k^{1-1}$$

Subtract 1 from 2.

$$4k^{3}+58k^{1}+42k^{1-1}$$

Subtract 1 from 1.

$$4k^{3}+58k^{1}+42k^{0}$$

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

$$4k^{3}+58k+42k^{0}$$

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

$$4k^{3}+58k+42\times 1$$

For any term t, t\times 1=t and 1t=t.

$$4k^{3}+58k+42$$

Evaluate

$$k^{4}+29k^{2}+42k+24$$

Solution Steps

Combine 6k^{2} and 23k^{2} to get 29k^{2}.

$$k^{4}+29k^{2}+42k+24$$