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Earn +20 ptsQ: What is the first derivative of e raised to the power of x?
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What is the derivative of e to the power of x?
The derivative of ex is ex
What is e raised to the 0th power?
e raised to the 0 power is 1
Why is the function ex the natural number e raised to the power of x so special from the calculus point of view?
That's because powers that involve the power "e", and logarithms to the base "e", are simpler than other powers or logarithms. For example: the derivative of ex is ex, while a derivative with other bases is more complicated; while the derivative of the natural logarithm (ln x, or logex) is 1/x.
What is the derivative of e to the power ln x squared?
e^[ln(x^2)]=x^2, so your question is really, "What is the derivative of x^2," to which the answer is 2x.
What is the anti derivative of e raised to 6?
Well the number e, raised to 6 (e^6) is just a number (a constant), so you integrate a constant times dx gives you that constant times x + C --> x*e^6 + C
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