Solve f(x)=-x^3+4x^2+5x-2

$$f ( x ) = - x ^ { 3 } + 4 x ^ { 2 } + 5 x - 2$$

Differentiate w.r.t. x

$$5+8x-3x^{2}$$

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}.

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

Multiply 3 times -1.

$$-3x^{3-1}+2\times 4x^{2-1}+5x^{1-1}$$

Subtract 1 from 3.

$$-3x^{2}+2\times 4x^{2-1}+5x^{1-1}$$

Multiply 2 times 4.

$$-3x^{2}+8x^{2-1}+5x^{1-1}$$

Subtract 1 from 2.

$$-3x^{2}+8x^{1}+5x^{1-1}$$

Subtract 1 from 1.

$$-3x^{2}+8x^{1}+5x^{0}$$

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

$$-3x^{2}+8x+5x^{0}$$

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

$$-3x^{2}+8x+5\times 1$$

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

$$-3x^{2}+8x+5$$

Evaluate

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