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Popular >

derivative of ln(sin(e^x))

Solution

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

Solution

e^{x} cot (e^{x})

Solution steps

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

Apply the chain rule:

\frac{1}{sin ( e ^{x} )} \frac{d}{d x} (sin (e^{x}))

= \frac{1}{sin ( e ^{x} )} \frac{d}{d x} (sin (e^{x}))

\frac{d}{d x} (sin (e^{x})) = cos (e^{x}) e^{x}

= \frac{1}{sin ( e ^{x} )} cos (e^{x}) e^{x}

Simplify

\frac{1}{sin ( e ^{x} )} cos (e^{x}) e^{x} : e^{x} cot (e^{x})

= e^{x} cot (e^{x})

Graph

Popular Examples

derivative of g(x)=ln(3x)derivative of

g (x) = ln (3 x)

derivative of 9x^{1/3}+9/2 x^{4/3}derivative of

9 x^{\frac{1}{3}} + \frac{9}{2} x^{\frac{4}{3}}

(\partial)/(\partial x)(-xe^{(xy)})

\frac{\partial}{\partial x} (- x e^{(x y)})

integral of-2x+18x^2-4x^3+C

\int - 2 x + 18 x^{2} - 4 x^{3} + C d x

integral of 2cos^3(x)sin(x)

\int 2 cos^{3} (x) sin (x) d x

Frequently Asked Questions (FAQ)

What is the derivative of ln(sin(e^x)) ?
The derivative of ln(sin(e^x)) is e^xcot(e^x)
What is the first derivative of ln(sin(e^x)) ?
The first derivative of ln(sin(e^x)) is e^xcot(e^x)