Solve x^5-2x^2-3-x-3

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

Differentiate w.r.t. x

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

Steps Using Derivative Rule for Sum

Subtract 3 from -3 to get -6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{5}-2x^{2}-6-x)$$

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}.

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

Subtract 1 from 5.

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

Multiply 2 times -2.

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

Subtract 1 from 2.

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

Subtract 1 from 1.

$$5x^{4}-4x^{1}-x^{0}$$

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

$$5x^{4}-4x-x^{0}$$

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

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

Evaluate

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

Solution Steps

Subtract 3 from -3 to get -6.

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