Solve 8x^9+12x^6+9x^3+1

$$8 x ^ { 9 } + 12 x ^ { 6 } + 9 x ^ { 3 } + 1$$

Differentiate w.r.t. x

$$72x^{8}+72x^{5}+27x^{2}$$

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}.

$$9\times 8x^{9-1}+6\times 12x^{6-1}+3\times 9x^{3-1}$$

Multiply 9 times 8.

$$72x^{9-1}+6\times 12x^{6-1}+3\times 9x^{3-1}$$

Subtract 1 from 9.

$$72x^{8}+6\times 12x^{6-1}+3\times 9x^{3-1}$$

Multiply 6 times 12.

$$72x^{8}+72x^{6-1}+3\times 9x^{3-1}$$

Subtract 1 from 6.

$$72x^{8}+72x^{5}+3\times 9x^{3-1}$$

Multiply 6 times 12.

$$72x^{8}+72x^{5}+27x^{3-1}$$

Subtract 1 from 3.

$$72x^{8}+72x^{5}+27x^{2}$$

Evaluate

$$8x^{9}+12x^{6}+9x^{3}+1$$