Solve (x^3+4x^2-2x+5)+(x^2+2x+1)

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

Evaluate

$$x^{3}+5x^{2}+6$$

Solution Steps

Combine 4x^{2} and x^{2} to get 5x^{2}.

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

Combine -2x and 2x to get 0.

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

Add 5 and 1 to get 6.

$$x^{3}+5x^{2}+6$$

Differentiate w.r.t. x

$$x\left(3x+10\right)$$

Steps Using Derivative Rule for Sum

Combine 4x^{2} and x^{2} to get 5x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}+5x^{2}-2x+5+2x+1)$$

Combine -2x and 2x to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}+5x^{2}+5+1)$$

Add 5 and 1 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}+5x^{2}+6)$$

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}.

$$3x^{3-1}+2\times 5x^{2-1}$$

Subtract 1 from 3.

$$3x^{2}+2\times 5x^{2-1}$$

Multiply 2 times 5.

$$3x^{2}+10x^{2-1}$$

Subtract 1 from 2.

$$3x^{2}+10x^{1}$$

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

$$3x^{2}+10x$$