Question
Download Solution PDFWhat is the derivative of \(\rm e^{e^x}\) with respect to ex?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFormula used:
\(\rm \frac{d}{dx} e^{x} = e^{x}\)
Differentiation of y with respect to x is given by dy/dx.
Calculation:
Let, f(x) = \(\rm e^{e^x}\)
d[f(x)] = d[\(\rm e^{e^x}\)]
⇒ d[f(x)] = \(\rm e^{e^x} e^x\) ----(1)
Again, let, g(x) = \(\rm e^x\)
⇒ d[g(x)] = d[\(\rm e^x\)] -----(2)
Hence, the required derivative
\(\rm \frac{d[f(x)]}{d[g(x)]}\)= \(\rm \frac{\rm e^{e^x} e^x}{e^x}\)
⇒ \(\rm \frac{d[f(x)]}{d[g(x)]}\) = \(\rm e^{e^x}\)
∴ The derivative of \(e^{e^x}\) with respect to ex is \(\rm e^{e^x}\)
Last updated on May 30, 2025
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