Solve g(x)=5x^3+5x^2-26x+83

$$g ( x ) = 5 x ^ { 3 } + 5 x ^ { 2 } - 26 x + 83$$

Differentiate w.r.t. x

$$15x^{2}+10x-26$$

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}.

$$3\times 5x^{3-1}+2\times 5x^{2-1}-26x^{1-1}$$

Multiply 3 times 5.

$$15x^{3-1}+2\times 5x^{2-1}-26x^{1-1}$$

Subtract 1 from 3.

$$15x^{2}+2\times 5x^{2-1}-26x^{1-1}$$

Multiply 2 times 5.

$$15x^{2}+10x^{2-1}-26x^{1-1}$$

Subtract 1 from 2.

$$15x^{2}+10x^{1}-26x^{1-1}$$

Subtract 1 from 1.

$$15x^{2}+10x^{1}-26x^{0}$$

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

$$15x^{2}+10x-26x^{0}$$

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

$$15x^{2}+10x-26$$

Evaluate

$$5x^{3}+5x^{2}-26x+83$$