What is (\partial)/(\partial x)(5tan(5x)) ?

The answer to (\partial)/(\partial x)(5tan(5x)) is 25sec^2(5x)

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(\partial)/(\partial x)(5tan(5x))

\frac{\partial}{\partial x} (5 tan (5 x))

25 sec^{2} (5 x)

Solution steps

\frac{\partial}{\partial x} (5 tan (5 x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{\partial}{\partial x} (tan (5 x))

Apply the chain rule:

sec^{2} (5 x) \frac{\partial}{\partial x} (5 x)

= sec^{2} (5 x) \frac{\partial}{\partial x} (5 x)

\frac{\partial}{\partial x} (5 x) = 5

= 5 sec^{2} (5 x) \cdot 5

Simplify

= 25 sec^{2} (5 x)

What is (\partial)/(\partial x)(5tan(5x)) ?
The answer to (\partial)/(\partial x)(5tan(5x)) is 25sec^2(5x)