What is the derivative of f(x)=6ln(sec(x)+tan(x)) ?

The derivative of f(x)=6ln(sec(x)+tan(x)) is -6/((sec(x)+tan(x))(-1+sin(x)))

What is the first derivative of f(x)=6ln(sec(x)+tan(x)) ?

The first derivative of f(x)=6ln(sec(x)+tan(x)) is -6/((sec(x)+tan(x))(-1+sin(x)))

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derivative of

f (x) = 6 ln (sec (x) + tan (x))

- \frac{6}{( sec ( x ) + tan ( x ) ) ( - 1 + sin ( x ) )}

Solution steps

\frac{d}{d x} (6 ln (sec (x) + tan (x)))

Take the constant out:

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

= 6 \frac{d}{d x} (ln (sec (x) + tan (x)))

Apply the chain rule:

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

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

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

= 6 \cdot \frac{1}{sec ( x ) + tan ( x )} (- \frac{1}{- 1 + sin ( x )})

Simplify

6 \cdot \frac{1}{sec ( x ) + tan ( x )} (- \frac{1}{- 1 + sin ( x )}) : - \frac{6}{( sec ( x ) + tan ( x ) ) ( - 1 + sin ( x ) )}

= - \frac{6}{( sec ( x ) + tan ( x ) ) ( - 1 + sin ( x ) )}

\int p (p + 5)^{7} d p

\int \frac{x}{x ^{2} + 6 x + 10} d x

\frac{d}{d x} (\frac{6 x ^{2} + 6 x + 8}{x})

y^{^{'}} + 6 (tan (6 x)) y = - cos (6 x)

\int 2^{x} (1 + 5^{x}) d x

What is the derivative of f(x)=6ln(sec(x)+tan(x)) ?
The derivative of f(x)=6ln(sec(x)+tan(x)) is -6/((sec(x)+tan(x))(-1+sin(x)))
What is the first derivative of f(x)=6ln(sec(x)+tan(x)) ?
The first derivative of f(x)=6ln(sec(x)+tan(x)) is -6/((sec(x)+tan(x))(-1+sin(x)))