What is the d/(dθ)(e^{tan(θ)}) ?

The d/(dθ)(e^{tan(θ)}) is e^{tan(θ)}sec^2(θ)

What is the first d/(dθ)(e^{tan(θ)}) ?

The first d/(dθ)(e^{tan(θ)}) is e^{tan(θ)}sec^2(θ)

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\frac{d}{d θ} (e^{t a n (θ)})

e^{t a n (θ)} sec^{2} (θ)

Solution steps

\frac{d}{d θ} (e^{t a n (θ)})

Apply the chain rule:

e^{t a n (θ)} \frac{d}{d θ} (tan (θ))

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

\frac{d}{d θ} (tan (θ)) = sec^{2} (θ)

= e^{t a n (θ)} sec^{2} (θ)

What is the d/(dθ)(e^{tan(θ)}) ?
The d/(dθ)(e^{tan(θ)}) is e^{tan(θ)}sec^2(θ)
What is the first d/(dθ)(e^{tan(θ)}) ?
The first d/(dθ)(e^{tan(θ)}) is e^{tan(θ)}sec^2(θ)