What is the derivative of tan(e^{4t})+e^{tan(4t)} ?

The derivative of tan(e^{4t})+e^{tan(4t)} is sec^2(e^{4t})e^{4t}*4+e^{tan(4t)}sec^2(4t)*4

What is the first derivative of tan(e^{4t})+e^{tan(4t)} ?

The first derivative of tan(e^{4t})+e^{tan(4t)} is sec^2(e^{4t})e^{4t}*4+e^{tan(4t)}sec^2(4t)*4

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derivative of

tan (e^{4 t}) + e^{t a n (4 t)}

sec^{2} (e^{4 t}) e^{4 t} \cdot 4 + e^{t a n (4 t)} sec^{2} (4 t) \cdot 4

Solution steps

\frac{d}{d t} (tan (e^{4 t}) + e^{t a n (4 t)})

Apply the Sum/Difference Rule:

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

= \frac{d}{d t} (tan (e^{4 t})) + \frac{d}{d t} (e^{t a n (4 t)})

\frac{d}{d t} (tan (e^{4 t})) = sec^{2} (e^{4 t}) e^{4 t} \cdot 4

\frac{d}{d t} (e^{t a n (4 t)}) = e^{t a n (4 t)} sec^{2} (4 t) \cdot 4

= sec^{2} (e^{4 t}) e^{4 t} \cdot 4 + e^{t a n (4 t)} sec^{2} (4 t) \cdot 4

What is the derivative of tan(e^{4t})+e^{tan(4t)} ?
The derivative of tan(e^{4t})+e^{tan(4t)} is sec^2(e^{4t})e^{4t}*4+e^{tan(4t)}sec^2(4t)*4
What is the first derivative of tan(e^{4t})+e^{tan(4t)} ?
The first derivative of tan(e^{4t})+e^{tan(4t)} is sec^2(e^{4t})e^{4t}*4+e^{tan(4t)}sec^2(4t)*4