Answer:
yw
Step-by-step explanation:
Let :ℝ→ℝ be given by ()= and consider the ln function. We can take the composition so that we have:
(ln∘)()=ln(^)=ln
Now, if we take the derivative, on the left hand side we use the chain rule and on the right hand side we differentiate as usual so that we have:
′()/()=ln
Now solving for ′() gives ′()=()ln so that ′()=^ln. This useful technique can be used to take derivatives of other functions: we compose the original function with the inverse and then differentiate on both sides and use the same idea we've used here, this technique can simplify many derivatives and save a lot of time in some situations.