Solve 2-x^2+x^4-5x+6

$$2 - x ^ { 2 } + x ^ { 4 } - 5 x + 6$$

Differentiate w.r.t. x

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

Steps Using Derivative Rule for Sum

Add 2 and 6 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8-x^{2}+x^{4}-5x)$$

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}.

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

Multiply 2 times -1.

$$-2x^{2-1}+4x^{4-1}-5x^{1-1}$$

Subtract 1 from 2.

$$-2x^{1}+4x^{4-1}-5x^{1-1}$$

Subtract 1 from 4.

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

Subtract 1 from 1.

$$-2x^{1}+4x^{3}-5x^{0}$$

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

$$-2x+4x^{3}-5x^{0}$$

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

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

Evaluate

$$x^{4}-x^{2}-5x+8$$

Solution Steps

Add 2 and 6 to get 8.

$$8-x^{2}+x^{4}-5x$$