What is the derivative of e^{tan(pix}) ?

The derivative of e^{tan(pix}) is e^{tan(pix)}sec^2(pix)pi

What is the first derivative of e^{tan(pix}) ?

The first derivative of e^{tan(pix}) is e^{tan(pix)}sec^2(pix)pi

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\frac{d}{d x} (e^{t a n (π x)})

e^{t a n (π x)} sec^{2} (π x) π

Solution steps

\frac{d}{d x} (e^{t a n (π x)})

Apply the chain rule:

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

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

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

= e^{t a n (π x)} sec^{2} (π x) π

What is the derivative of e^{tan(pix}) ?
The derivative of e^{tan(pix}) is e^{tan(pix)}sec^2(pix)pi
What is the first derivative of e^{tan(pix}) ?
The first derivative of e^{tan(pix}) is e^{tan(pix)}sec^2(pix)pi