- #1
greg_rack
Gold Member
- 363
- 79
- Homework Statement
- Find the derivative of:
$$f(x)=\frac{\sqrt{ax}}{\sqrt{ax}-1}$$
- Relevant Equations
- Theorems of the algebra of derivatives
First, I calculated the derivative of
$$D(\sqrt{ax})=\frac{a}{2\sqrt{ax}}$$
Then, by applying the due theorems, I calculated the deriv of the whole function as follows:
$$
f'(x)=\frac{\frac{a}{2\sqrt{ax}}(\sqrt{ax}-1)-\sqrt{ax}(\frac{a}{2\sqrt{ax}})}{(\sqrt{ax}-1)^2}=
-\frac{a}{2\sqrt{ax}(\sqrt{ax}-1)^2}$$
Which is not the correct result I should get.
$$D(\sqrt{ax})=\frac{a}{2\sqrt{ax}}$$
Then, by applying the due theorems, I calculated the deriv of the whole function as follows:
$$
f'(x)=\frac{\frac{a}{2\sqrt{ax}}(\sqrt{ax}-1)-\sqrt{ax}(\frac{a}{2\sqrt{ax}})}{(\sqrt{ax}-1)^2}=
-\frac{a}{2\sqrt{ax}(\sqrt{ax}-1)^2}$$
Which is not the correct result I should get.