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Earn +20 ptsQ: What is the derivative of e to the power ln x squared?
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What is the first derivative of e raised to the power of x?
The first derivative of e to the x power is e to the power of x.
What is the derivative of e to the power of x?
The derivative of ex is ex
What is the anti derivative of 1 over x?
The anti-derivative of 1/x is ln|x| + C, where ln refers to logarithm of x to the base e and |x| refers to the absolute value of x, and C is a constant.
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.
Solve e raised to the power of negative x equals 6?
e-x = 6Take the natural log of both sides:ln(e-x) = ln(6)-x = ln(6)x = -ln(6)So x = -ln(6), which is about -1.792.
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