What is the derivative of tan(e^{7x}+e^{tan(7x)}) ?

The derivative of tan(e^{7x}+e^{tan(7x)}) is sec^2(e^{7x})e^{7x}*7+e^{tan(7x)}sec^2(7x)*7

What is the first derivative of tan(e^{7x}+e^{tan(7x)}) ?

The first derivative of tan(e^{7x}+e^{tan(7x)}) is sec^2(e^{7x})e^{7x}*7+e^{tan(7x)}sec^2(7x)*7

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\frac{d}{d x} (tan (e^{7 x}) + e^{t a n (7 x)})

sec^{2} (e^{7 x}) e^{7 x} \cdot 7 + e^{t a n (7 x)} sec^{2} (7 x) \cdot 7

Solution steps

\frac{d}{d x} (tan (e^{7 x}) + e^{t a n (7 x)})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (tan (e^{7 x})) + \frac{d}{d x} (e^{t a n (7 x)})

\frac{d}{d x} (tan (e^{7 x})) = sec^{2} (e^{7 x}) e^{7 x} \cdot 7

\frac{d}{d x} (e^{t a n (7 x)}) = e^{t a n (7 x)} sec^{2} (7 x) \cdot 7

= sec^{2} (e^{7 x}) e^{7 x} \cdot 7 + e^{t a n (7 x)} sec^{2} (7 x) \cdot 7

What is the derivative of tan(e^{7x}+e^{tan(7x)}) ?
The derivative of tan(e^{7x}+e^{tan(7x)}) is sec^2(e^{7x})e^{7x}*7+e^{tan(7x)}sec^2(7x)*7
What is the first derivative of tan(e^{7x}+e^{tan(7x)}) ?
The first derivative of tan(e^{7x}+e^{tan(7x)}) is sec^2(e^{7x})e^{7x}*7+e^{tan(7x)}sec^2(7x)*7