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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Multiply fractions:

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

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

\int (\frac{10}{x} + 10 x) d x

x \to 0 lim (\frac{x ( x )}{x + x})

f (x) = (3 x + 7)^{2}

\frac{d}{d x} f (x) = (5 x - 5 x^{3}) (7 + x)

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