Use logarithmic differentiation to calculate the derivative...

e^2x multiplied by sqrt(1+x^2) divided by tan(x)^2

Question

Use logarithmic differentiation to calculate the derivative...

e^2x multiplied by sqrt(1+x^2) divided by tan(x)^2

anonymous · Answer

$$2x+\log(\sqrt{1+x^2}))-2logtanx$$$$\frac{dy}{dx}=2+\frac{1}{\sqrt{1+x^2}}(2x)-2(\frac{1}{tanx})(\sec^2x)$$

anonymous · Answer

That's the answer i got but according to my teacher the  
$$2+ x \div 1+x ^{2}- 4\csc2x$$

anonymous · Answer

and thats multiplied by the original equation

anonymous · Answer

i think what Johnny has worked out is dy/d x * 1/y   (where y = f(x)

anonymous · Answer

i answered your question in your last post lilon

anonymous · Answer

i've had another look at this lilon and the answer according to your teacher is right
= as you say multiplied by the original equation

dy/dx = e^2x[2 +2x^2 + x - 4(1 + x^2)csc2x] / (1+x^2)^1/2*tan(x)^2