Calculus
posted by Anonymous .
For 0 < x < PI/2, if y = sin(x)^x, then dy/dx is..
I understand that you can take the natural logarithm of both sides and then take the derivative but why can't I simply take the derivative of it and get.. dy/dx = x(cos(x))(sin(x))^(x1).
Thanks in advance :).

Oh that was silly >.>.. I can't apply the power rule since it doesn't have a constant exponent. So is the only way to differentiate this equation is to use the natural logarithm and then the power + chain rule?
Respond to this Question
Similar Questions

Calculus> bobpursley
How do you get m=0? from taking the second derivative? 
Calculus
If I have a function f(x), and am given its derivative, f'(x): may I take it as a given that f(x) is an integral of f'(x). My reasoning is that 'undoing' the derivative gives me the derivative. Eg is 1/3x^3 an integral of x^2? 
Calculus
If x = t^2 + 1 and y = t^3, then d^2y/dx^2 = I know I can solve for t in terms of x and substitute that into y = t^3 and find the double derivative. I also know that I can take the derivative of x and y then divide dy/dt by dx/dt. … 
calculus
Could someone check my reasoning? thanx Find the derivative of the function. sin(sin[sinx]) I need to use the chain rule to solve. So I take the derivative sin(sin[sinx) first. Then multiply that by the inside which is the derivative 
Calculus
Find f'(c) if f(x)=3e^(x+2)+ e^(5) [NOTE:A small algebraic manipulation is needed first to get f(x) into a form so that the derivative can be taken and your answer isn't a # but rather a formula that returns and answer.] attempt … 
Math
I understand generally how to solve, by taking natural logs and the the derivative, but i am confused by the presence of the 3 in front... if f(x)= 3(sin(x))^x, find f'(1) should i move 3 to the y side or take the natural log of it? 
calculus
Differentiate both sides of the double angle identify sin 2x= 2 sin x cos x to determine an identify for cos x. Find the first derivative, second derivative, third fourth, fifth, sixth, seventh and eighth derivative. Use the results … 
urgent urgent algebra / precalculas
For # 1, im getting stuck on this problem i don't understand this 1.4 = e ^ (0.03k) Now take the natural logarithm of both sides to solve for , ln 1.4 = ln e ^ (0.03k) ln 1.4 = 0.03k * ln e Recall that ln e = 1. ln 1.4 = 0.03 k Solve … 
applied calculus
1. Consider the function y = xx (for x> 0). a) Why does the derivative rule for xn not apply? 
Calculus
What would an example of a logarithmic function that contains two trig functions within it where you would need to use chain rule and product rule to take derivative look like?