What is (\partial)/(\partial y)(e^{sin(x+y)}) ?

The answer to (\partial)/(\partial y)(e^{sin(x+y)}) is e^{sin(x+y)}cos(x+y)

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(\partial)/(\partial y)(e^{sin(x+y)})

\frac{\partial}{\partial y} (e^{s i n (x + y)})

e^{s i n (x + y)} cos (x + y)

Solution steps

\frac{\partial}{\partial y} (e^{s i n (x + y)})

Treat

x

as a constant

Apply the chain rule:

e^{s i n (x + y)} \frac{\partial}{\partial y} (sin (x + y))

= e^{s i n (x + y)} \frac{\partial}{\partial y} (sin (x + y))

\frac{\partial}{\partial y} (sin (x + y)) = cos (x + y)

= e^{s i n (x + y)} cos (x + y)

f (x) = 1 + 4 csc (x), at x = - \frac{π}{3}

n = 1 \sum \infty \frac{2}{3 n + 10}

\int_{1}^{2} 4 x 4 x^{2} + 4 d x

\int (3 x^{4} - 5 x^{2} + 6 x) d x

x \to 0 lim (\frac{∣ x + 1 ∣ - ∣ x - 1 ∣}{x})

What is (\partial)/(\partial y)(e^{sin(x+y)}) ?
The answer to (\partial)/(\partial y)(e^{sin(x+y)}) is e^{sin(x+y)}cos(x+y)