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

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

Differentiate w.r.t. x

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

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}.

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

Subtract 1 from 2.

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

Subtract 1 from 1.

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

Multiply 1 times -5.

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

Subtract 1 from 3.

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

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

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

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

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

Evaluate

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