Solve F(-6)=6x^3+12x^2-50x+1

$$F ( - 6 ) = 6 x ^ { 3 } + 12 x ^ { 2 } - 50 x + 1$$

Differentiate w.r.t. x

$$18x^{2}+24x-50$$

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}.

$$3\times 6x^{3-1}+2\times 12x^{2-1}-50x^{1-1}$$

Multiply 3 times 6.

$$18x^{3-1}+2\times 12x^{2-1}-50x^{1-1}$$

Subtract 1 from 3.

$$18x^{2}+2\times 12x^{2-1}-50x^{1-1}$$

Multiply 2 times 12.

$$18x^{2}+24x^{2-1}-50x^{1-1}$$

Subtract 1 from 2.

$$18x^{2}+24x^{1}-50x^{1-1}$$

Subtract 1 from 1.

$$18x^{2}+24x^{1}-50x^{0}$$

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

$$18x^{2}+24x-50x^{0}$$

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

$$18x^{2}+24x-50$$

Evaluate

$$6x^{3}+12x^{2}-50x+1$$