Solve /100r^2-220r+121

$$\frac{ }{ 100 { r }^{ 2 } -220r+121 }$$

Differentiate w.r.t. r

$$-\frac{20}{\left(10r-11\right)^{3}}$$

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).

$$-\left(100r^{2}-220r^{1}+121\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}r}(100r^{2}-220r^{1}+121)$$

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}.

$$-\left(100r^{2}-220r^{1}+121\right)^{-2}\left(2\times 100r^{2-1}-220r^{1-1}\right)$$

Simplify.

$$\left(100r^{2}-220r^{1}+121\right)^{-2}\left(-200r^{1}+220r^{0}\right)$$

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

$$\left(100r^{2}-220r+121\right)^{-2}\left(-200r+220r^{0}\right)$$

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

$$\left(100r^{2}-220r+121\right)^{-2}\left(-200r+220\times 1\right)$$

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

$$\left(100r^{2}-220r+121\right)^{-2}\left(-200r+220\right)$$

Evaluate

$$\frac{1}{\left(10r-11\right)^{2}}$$