Solve x^4-5x^2-5x^2+23x+10

$$x ^ { 4 } - 5 x ^ { 2 } - 5 x ^ { 2 } + 23 x + 10$$

Differentiate w.r.t. x

$$4x^{3}-20x+23$$

Steps Using Derivative Rule for Sum

Combine -5x^{2} and -5x^{2} to get -10x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}-10x^{2}+23x+10)$$

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}.

$$4x^{4-1}+2\left(-10\right)x^{2-1}+23x^{1-1}$$

Subtract 1 from 4.

$$4x^{3}+2\left(-10\right)x^{2-1}+23x^{1-1}$$

Multiply 2 times -10.

$$4x^{3}-20x^{2-1}+23x^{1-1}$$

Subtract 1 from 2.

$$4x^{3}-20x^{1}+23x^{1-1}$$

Subtract 1 from 1.

$$4x^{3}-20x^{1}+23x^{0}$$

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

$$4x^{3}-20x+23x^{0}$$

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

$$4x^{3}-20x+23\times 1$$

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

$$4x^{3}-20x+23$$

Evaluate

$$x^{4}-10x^{2}+23x+10$$

Solution Steps

Combine -5x^{2} and -5x^{2} to get -10x^{2}.

$$x^{4}-10x^{2}+23x+10$$