What is the derivative of e^ysin(x) ?

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

\int \frac{3}{x 1 + 2 x} d x

\int 5 x (sin (x)) d x

\frac{d}{d x} (2 sec (x) + cot (x))

\int \frac{x + 1}{x} d x

\frac{d}{d x} (ln (arcsin (cos (x))))

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