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Popular >

derivative of tan(e^{3x}+e^{tan(3x)})

Solution

\frac{d}{d x} (tan (e^{3 x}) + e^{t a n (3 x)})

Solution

sec^{2} (e^{3 x}) e^{3 x} \cdot 3 + e^{t a n (3 x)} sec^{2} (3 x) \cdot 3

Solution steps

\frac{d}{d x} (tan (e^{3 x}) + e^{t a n (3 x)})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (tan (e^{3 x})) + \frac{d}{d x} (e^{t a n (3 x)})

\frac{d}{d x} (tan (e^{3 x})) = sec^{2} (e^{3 x}) e^{3 x} \cdot 3

\frac{d}{d x} (e^{t a n (3 x)}) = e^{t a n (3 x)} sec^{2} (3 x) \cdot 3

= sec^{2} (e^{3 x}) e^{3 x} \cdot 3 + e^{t a n (3 x)} sec^{2} (3 x) \cdot 3

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of tan(e^{3x}+e^{tan(3x)}) ?
The derivative of tan(e^{3x}+e^{tan(3x)}) is sec^2(e^{3x})e^{3x}*3+e^{tan(3x)}sec^2(3x)*3
What is the first derivative of tan(e^{3x}+e^{tan(3x)}) ?
The first derivative of tan(e^{3x}+e^{tan(3x)}) is sec^2(e^{3x})e^{3x}*3+e^{tan(3x)}sec^2(3x)*3