How to Differentiate Number Raised to Power of x?

How to differentiate something raised to the power of x? We can first apply the logarithmic rule to take the x down from the exponent. Then, we apply implicit differentiation by taking the derivative on every term with respect to x, and solve for dy/dx. Substitute the original function into 'y' and we got the final answer.
Implicit Differentiation Explanation: • Learn Implicit Differe...
0:00 Logarithmic Rule
0:22 Taking Natural Log on Both Sides
0:33 Applying Implicit Differentiation
0:54 Solve for dy/dx
1:08 Substitute function y into equation

[@Qermaq]

Never heard ln pronounced "lawn" before.

[@eshanaayushman933]

Its actually also a general formula:
d(a^x)/dx = a^x(ln(a))

[@leontsc4352]

Why you have only a hundred subscribers 😭😭😭
PS: I really like your videos please don't ever stop doing them

[@YeahMathIsBoring]

I just started this channel a month ago. Thanks for your support anyway! I'll be uploading as frequent as I could.

[@bruhifysbackup]

Use first principles.

[@DarkTouch]

not a fan of lawn. just call it log. log = ln. if the base is not e, then say log base b. we just get rid of bases not e anyway in most applications.

[@zai6965]

Couldn’t you just use chain rule?

[@YeahMathIsBoring]

Actually, chain can be used as well!

[@YeahMathIsBoring]

You just have to rewrite the function into e^(ln 2^x). It's equivalent to 2^x. After rewrite it into e^(ln 2^x), we can bring the x down using logarithm property, and it would be e^( x*(ln 2) ). Then, we can differentiate this exponential functions using chain rule and still be getting the same answer.