What is the derivative of ln(sec(5x)+tan(5x)) ?

The derivative of ln(sec(5x)+tan(5x)) is 5sec(5x)

What is the first derivative of ln(sec(5x)+tan(5x)) ?

The first derivative of ln(sec(5x)+tan(5x)) is 5sec(5x)

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derivative of

ln (sec (5 x) + tan (5 x))

5 sec (5 x)

Solution steps

\frac{d}{d x} (ln (sec (5 x) + tan (5 x)))

Apply the chain rule:

\frac{1}{sec ( 5 x ) + tan ( 5 x )} \frac{d}{d x} (sec (5 x) + tan (5 x))

= \frac{1}{sec ( 5 x ) + tan ( 5 x )} \frac{d}{d x} (sec (5 x) + tan (5 x))

\frac{d}{d x} (sec (5 x) + tan (5 x)) = sec (5 x) tan (5 x) \cdot 5 + sec^{2} (5 x) \cdot 5

= \frac{1}{sec ( 5 x ) + tan ( 5 x )} (sec (5 x) tan (5 x) \cdot 5 + sec^{2} (5 x) \cdot 5)

Simplify

\frac{1}{sec ( 5 x ) + tan ( 5 x )} (sec (5 x) tan (5 x) \cdot 5 + sec^{2} (5 x) \cdot 5) : 5 sec (5 x)

= 5 sec (5 x)

\int 5 \frac{cos ( x ) + sin ( 2 x )}{sin ( x )} d x

n = 1 \sum \infty 8 (- \frac{1}{4})^{n}

x \to 0 + lim (2 x ln (x))

x^{2} + 4, - x^{2} - 1, x = - 2, x = 3

f (x) = x^{2} ln (2 x)

What is the derivative of ln(sec(5x)+tan(5x)) ?
The derivative of ln(sec(5x)+tan(5x)) is 5sec(5x)
What is the first derivative of ln(sec(5x)+tan(5x)) ?
The first derivative of ln(sec(5x)+tan(5x)) is 5sec(5x)