Solve =1/s^2+2s+1

$$= \frac { 1 } { s ^ { 2 } + 2 s + 1 }$$

Differentiate w.r.t. s

$$-\frac{2}{\left(s+1\right)^{3}}$$

Steps Using Chain Rule

If F is the composition of two differentiable functions f\left(u\right) and u=g\left(x\right), that is, if F\left(x\right)=f\left(g\left(x\right)\right), then the derivative of F is the derivative of f with respect to u times the derivative of g with respect to x, that is, \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right).

$$-\left(s^{2}+2s^{1}+1\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}s}(s^{2}+2s^{1}+1)$$

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}.

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

Simplify.

$$\left(s^{2}+2s^{1}+1\right)^{-2}\left(-2s^{1}-2s^{0}\right)$$

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

$$\left(s^{2}+2s+1\right)^{-2}\left(-2s-2s^{0}\right)$$

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

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

Evaluate

$$\frac{1}{\left(s+1\right)^{2}}$$