Solve (x^5-2x^2+3x^2+10x-4)

$$( x ^ { 5 } - 2 x ^ { 2 } + 3 x ^ { 2 } + 10 x - 4 )$$

Differentiate w.r.t. x

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

Steps Using Derivative Rule for Sum

Combine -2x^{2} and 3x^{2} to get x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{5}+x^{2}+10x-4)$$

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}.

$$5x^{5-1}+2x^{2-1}+10x^{1-1}$$

Subtract 1 from 5.

$$5x^{4}+2x^{2-1}+10x^{1-1}$$

Subtract 1 from 2.

$$5x^{4}+2x^{1}+10x^{1-1}$$

Subtract 1 from 1.

$$5x^{4}+2x^{1}+10x^{0}$$

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

$$5x^{4}+2x+10x^{0}$$

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

$$5x^{4}+2x+10\times 1$$

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

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

Evaluate

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

Solution Steps

Combine -2x^{2} and 3x^{2} to get x^{2}.

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