What is the derivative of tan(e^{9t})+e^{tan(9t)} ?

The derivative of tan(e^{9t})+e^{tan(9t)} is sec^2(e^{9t})e^{9t}*9+e^{tan(9t)}sec^2(9t)*9

What is the first derivative of tan(e^{9t})+e^{tan(9t)} ?

The first derivative of tan(e^{9t})+e^{tan(9t)} is sec^2(e^{9t})e^{9t}*9+e^{tan(9t)}sec^2(9t)*9

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derivative of

tan (e^{9 t}) + e^{t a n (9 t)}

sec^{2} (e^{9 t}) e^{9 t} \cdot 9 + e^{t a n (9 t)} sec^{2} (9 t) \cdot 9

Solution steps

\frac{d}{d t} (tan (e^{9 t}) + e^{t a n (9 t)})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d t} (tan (e^{9 t})) + \frac{d}{d t} (e^{t a n (9 t)})

\frac{d}{d t} (tan (e^{9 t})) = sec^{2} (e^{9 t}) e^{9 t} \cdot 9

\frac{d}{d t} (e^{t a n (9 t)}) = e^{t a n (9 t)} sec^{2} (9 t) \cdot 9

= sec^{2} (e^{9 t}) e^{9 t} \cdot 9 + e^{t a n (9 t)} sec^{2} (9 t) \cdot 9

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What is the derivative of tan(e^{9t})+e^{tan(9t)} ?
The derivative of tan(e^{9t})+e^{tan(9t)} is sec^2(e^{9t})e^{9t}*9+e^{tan(9t)}sec^2(9t)*9
What is the first derivative of tan(e^{9t})+e^{tan(9t)} ?
The first derivative of tan(e^{9t})+e^{tan(9t)} is sec^2(e^{9t})e^{9t}*9+e^{tan(9t)}sec^2(9t)*9