Solve 3-2x^5+6x^3-4x^6?

$$3 - 2 x ^ { 5 } + 6 x ^ { 3 } - 4 x ^ { 6 } ?$$

Differentiate w.r.t. x

$$18x^{2}-10x^{4}-24x^{5}$$

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}.

$$5\left(-2\right)x^{5-1}+3\times 6x^{3-1}+6\left(-4\right)x^{6-1}$$

Multiply 5 times -2.

$$-10x^{5-1}+3\times 6x^{3-1}+6\left(-4\right)x^{6-1}$$

Subtract 1 from 5.

$$-10x^{4}+3\times 6x^{3-1}+6\left(-4\right)x^{6-1}$$

Multiply 3 times 6.

$$-10x^{4}+18x^{3-1}+6\left(-4\right)x^{6-1}$$

Subtract 1 from 3.

$$-10x^{4}+18x^{2}+6\left(-4\right)x^{6-1}$$

Multiply 3 times 6.

$$-10x^{4}+18x^{2}-24x^{6-1}$$

Subtract 1 from 6.

$$-10x^{4}+18x^{2}-24x^{5}$$

Evaluate

$$3+6x^{3}-2x^{5}-4x^{6}$$