What is the derivative of f(x)=csc(sqrt(x+5)) ?

The derivative of f(x)=csc(sqrt(x+5)) is -(cot(sqrt(x+5))csc(sqrt(x+5)))/(2sqrt(x+5))

What is the first derivative of f(x)=csc(sqrt(x+5)) ?

The first derivative of f(x)=csc(sqrt(x+5)) is -(cot(sqrt(x+5))csc(sqrt(x+5)))/(2sqrt(x+5))

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derivative of

f (x) = csc (x + 5)

- \frac{cot ( x + 5 ) csc ( x + 5 )}{2 x + 5}

Solution steps

\frac{d}{d x} (csc (x + 5))

Apply the chain rule:

- cot (x + 5) csc (x + 5) \frac{d}{d x} (x + 5)

= - cot (x + 5) csc (x + 5) \frac{d}{d x} (x + 5)

\frac{d}{d x} (x + 5) = \frac{1}{2 x + 5}

= - cot (x + 5) csc (x + 5) \frac{1}{2 x + 5}

Simplify

- cot (x + 5) csc (x + 5) \frac{1}{2 x + 5} : - \frac{cot ( x + 5 ) csc ( x + 5 )}{2 x + 5}

= - \frac{cot ( x + 5 ) csc ( x + 5 )}{2 x + 5}

\frac{d}{d x} (ln (\frac{5 x + 2}{5 x - 2}))

f (x) = \frac{1}{3 x + 1}

y^{^{'}} = t e^{- y}, y (0) = 1

\int_{0}^{1} cos (2 π x) d x

x \to 3 lim (x - 1)

What is the derivative of f(x)=csc(sqrt(x+5)) ?
The derivative of f(x)=csc(sqrt(x+5)) is -(cot(sqrt(x+5))csc(sqrt(x+5)))/(2sqrt(x+5))
What is the first derivative of f(x)=csc(sqrt(x+5)) ?
The first derivative of f(x)=csc(sqrt(x+5)) is -(cot(sqrt(x+5))csc(sqrt(x+5)))/(2sqrt(x+5))