What is the derivative of sin(e^{sqrt(x)}) ?

The derivative of sin(e^{sqrt(x)}) is (e^{sqrt(x)}cos(e^{sqrt(x)}))/(2sqrt(x))

What is the first derivative of sin(e^{sqrt(x)}) ?

The first derivative of sin(e^{sqrt(x)}) is (e^{sqrt(x)}cos(e^{sqrt(x)}))/(2sqrt(x))

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

\frac{e ^{x} cos ( e ^{x} )}{2 x}

Solution steps

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

Apply the chain rule:

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

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

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

= cos (e^{x}) \frac{e ^{x}}{2 x}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{e ^{x} cos ( e ^{x} )}{2 x}

\frac{d}{d θ} (e^{2 θ})

\int \frac{1}{x ( ln ( x ^{2} ) )} d x

\int ln (e^{x y} cos (x)) d y

\int x^{4} a x^{5} - b d x

\frac{\partial}{\partial x} (ln (x + 6 y + 9 z))

What is the derivative of sin(e^{sqrt(x)}) ?
The derivative of sin(e^{sqrt(x)}) is (e^{sqrt(x)}cos(e^{sqrt(x)}))/(2sqrt(x))
What is the first derivative of sin(e^{sqrt(x)}) ?
The first derivative of sin(e^{sqrt(x)}) is (e^{sqrt(x)}cos(e^{sqrt(x)}))/(2sqrt(x))