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Prove d/dx(a^x) = a^x ina

User Cuneyt
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4 votes

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.

User Fencepost
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