What is the derivative of e^xsin(y) ?

The derivative of e^xsin(y) is e^xsin(y)+cos(y)(dy)/(dx)e^x

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

The first derivative of e^xsin(y) is e^xsin(y)+cos(y)(dy)/(dx)e^x

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

x \to - 1 lim (x^{2} - 1)

n = 0 \sum \infty \frac{2}{5 ^{n - 1}}

y = sin (sin (x)), (3 π, 0)

(- x)^{^{'}}

\frac{d}{d x} ((\frac{4}{5} x)^{3})

What is the derivative of e^xsin(y) ?
The derivative of e^xsin(y) is e^xsin(y)+cos(y)(dy)/(dx)e^x
What is the first derivative of e^xsin(y) ?
The first derivative of e^xsin(y) is e^xsin(y)+cos(y)(dy)/(dx)e^x