What is the derivative of sqrt(csc(3e^x)) ?

The derivative of sqrt(csc(3e^x)) is -(3e^xcot(3e^x)sqrt(csc(3e^x)))/2

What is the first derivative of sqrt(csc(3e^x)) ?

The first derivative of sqrt(csc(3e^x)) is -(3e^xcot(3e^x)sqrt(csc(3e^x)))/2

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Popular >

\frac{d}{d x} (csc (3 e^{x}))

- \frac{3 e ^{x} cot ( 3 e ^{x} ) csc ( 3 e ^{x} )}{2}

Solution steps

\frac{d}{d x} (csc (3 e^{x}))

Apply the chain rule:

\frac{1}{2 csc ( 3 e ^{x} )} \frac{d}{d x} (csc (3 e^{x}))

= \frac{1}{2 csc ( 3 e ^{x} )} \frac{d}{d x} (csc (3 e^{x}))

\frac{d}{d x} (csc (3 e^{x})) = - cot (3 e^{x}) csc (3 e^{x}) \cdot 3 e^{x}

= \frac{1}{2 csc ( 3 e ^{x} )} (- cot (3 e^{x}) csc (3 e^{x}) \cdot 3 e^{x})

Simplify

\frac{1}{2 csc ( 3 e ^{x} )} (- cot (3 e^{x}) csc (3 e^{x}) \cdot 3 e^{x}) : - \frac{3 e ^{x} cot ( 3 e ^{x} ) csc ( 3 e ^{x} )}{2}

= - \frac{3 e ^{x} cot ( 3 e ^{x} ) csc ( 3 e ^{x} )}{2}

\frac{d}{d x} (e^{x} x^{e})

\frac{d}{d x} (3^{s i n (x^{3})})

\int x^{5} \cdot e^{x} d x

\int \frac{t + 1}{t} d t

(x, y) \to (0, 0) lim ((x^{2} + y^{2}) ln (x^{2} + y^{2}))

What is the derivative of sqrt(csc(3e^x)) ?
The derivative of sqrt(csc(3e^x)) is -(3e^xcot(3e^x)sqrt(csc(3e^x)))/2
What is the first derivative of sqrt(csc(3e^x)) ?
The first derivative of sqrt(csc(3e^x)) is -(3e^xcot(3e^x)sqrt(csc(3e^x)))/2