What is (\partial)/(\partial x)(sin(x)+x^2e^y-1) ?

The answer to (\partial)/(\partial x)(sin(x)+x^2e^y-1) is 2e^yx+cos(x)

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(\partial)/(\partial x)(sin(x)+x^2e^y-1)

\frac{\partial}{\partial x} (sin (x) + x^{2} e^{y} - 1)

2 e^{y} x + cos (x)

Solution steps

\frac{\partial}{\partial x} (sin (x) + x^{2} e^{y} - 1)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (sin (x)) + \frac{\partial}{\partial x} (x^{2} e^{y}) - \frac{\partial}{\partial x} (1)

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

\frac{\partial}{\partial x} (x^{2} e^{y}) = 2 e^{y} x

\frac{\partial}{\partial x} (1) = 0

= cos (x) + 2 e^{y} x - 0

Simplify

= 2 e^{y} x + cos (x)

f (x) = \frac{ln ( x )}{x ^{3}}

x \to 0.01 lim (a x^{2} - x + b)

\int cos (x) (9 + 5 sin^{2} (x)) d x

\int sin (x y) + x y cos (x y) d x

\int_{3}^{7} \frac{( 2 x - 3 )}{6} d x

What is (\partial)/(\partial x)(sin(x)+x^2e^y-1) ?
The answer to (\partial)/(\partial x)(sin(x)+x^2e^y-1) is 2e^yx+cos(x)