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

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

Differentiate w.r.t. x

$$3x^{2}-12x+5$$

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}.

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

Subtract 1 from 1.

$$5x^{0}+3x^{3-1}+2\left(-6\right)x^{2-1}$$

Subtract 1 from 3.

$$5x^{0}+3x^{2}+2\left(-6\right)x^{2-1}$$

Multiply 3 times 1.

$$5x^{0}+3x^{2}-12x^{2-1}$$

Subtract 1 from 2.

$$5x^{0}+3x^{2}-12x^{1}$$

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

$$5x^{0}+3x^{2}-12x$$

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

$$5\times 1+3x^{2}-12x$$

For any term t, t\times 1=t and 1t=t.

$$5+3x^{2}-12x$$

Evaluate

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