What is the derivative of f(y)=e^{tan(x)} ?

The derivative of f(y)=e^{tan(x)} is e^{tan(x)}sec^2(x)

What is the first derivative of f(y)=e^{tan(x)} ?

The first derivative of f(y)=e^{tan(x)} is e^{tan(x)}sec^2(x)

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derivative of

f (y) = e^{t a n (x)}

e^{t a n (x)} sec^{2} (x)

Solution steps

\frac{d}{d x} (e^{t a n (x)})

Apply the chain rule:

e^{t a n (x)} \frac{d}{d x} (tan (x))

= e^{t a n (x)} \frac{d}{d x} (tan (x))

\frac{d}{d x} (tan (x)) = sec^{2} (x)

= e^{t a n (x)} sec^{2} (x)

What is the derivative of f(y)=e^{tan(x)} ?
The derivative of f(y)=e^{tan(x)} is e^{tan(x)}sec^2(x)
What is the first derivative of f(y)=e^{tan(x)} ?
The first derivative of f(y)=e^{tan(x)} is e^{tan(x)}sec^2(x)