What is (\partial)/(\partial x)(e^x+cos(xy)) ?

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

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(\partial)/(\partial x)(e^x+cos(xy))

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

e^{x} - sin (x y) y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= e^{x} - sin (x y) y

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

\int \frac{2 x}{9 - x ^{4}} d x

(- 3, 1), (- 7, - 2)

(sec (x))^{3}

\int \frac{e ^{x}}{( e ^{x} - 8 ) ( e ^{2 x} + 1 )} d x

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