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

The derivative of e^xcos(sqrt(x)) is e^xcos(sqrt(x))-(e^xsin(sqrt(x)))/(2sqrt(x))

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

The first derivative of e^xcos(sqrt(x)) is e^xcos(sqrt(x))-(e^xsin(sqrt(x)))/(2sqrt(x))

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

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x}, g = cos (x)

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

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

\frac{d}{d x} (cos (x)) = - \frac{sin ( x )}{2 x}

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

Simplify

e^{x} cos (x) + (- \frac{sin ( x )}{2 x}) e^{x} : e^{x} cos (x) - \frac{e ^{x} sin ( x )}{2 x}

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

\frac{d}{d x} (ln (e^{x} + 7 x + 1))

\frac{\partial}{\partial r} (r \cdot cos (t))

\int_{2}^{1} 12 x^{- 5} d x

\frac{d}{d x} ((x - \frac{1}{x})^{2})

\int sin (\frac{π}{2} x) d x

What is the derivative of e^xcos(sqrt(x)) ?
The derivative of e^xcos(sqrt(x)) is e^xcos(sqrt(x))-(e^xsin(sqrt(x)))/(2sqrt(x))
What is the first derivative of e^xcos(sqrt(x)) ?
The first derivative of e^xcos(sqrt(x)) is e^xcos(sqrt(x))-(e^xsin(sqrt(x)))/(2sqrt(x))