Solve x^4+3x^6-2x-10

$$x ^ { 4 } + 3 x ^ { 6 } - 2 x - 10$$

Differentiate w.r.t. x

$$18x^{5}+4x^{3}-2$$

Steps Using Derivative Rule for Sum

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}.

$$4x^{4-1}+6\times 3x^{6-1}-2x^{1-1}$$

Subtract 1 from 4.

$$4x^{3}+6\times 3x^{6-1}-2x^{1-1}$$

Multiply 6 times 3.

$$4x^{3}+18x^{6-1}-2x^{1-1}$$

Subtract 1 from 6.

$$4x^{3}+18x^{5}-2x^{1-1}$$

Subtract 1 from 1.

$$4x^{3}+18x^{5}-2x^{0}$$

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

$$4x^{3}+18x^{5}-2$$

Evaluate

$$3x^{6}+x^{4}-2x-10$$