What is (\partial)/(\partial x)(x^3e^y+cos(y)) ?

The answer to (\partial)/(\partial x)(x^3e^y+cos(y)) is 3e^yx^2

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(\partial)/(\partial x)(x^3e^y+cos(y))

\frac{\partial}{\partial x} (x^{3} e^{y} + cos (y))

3 e^{y} x^{2}

Solution steps

\frac{\partial}{\partial x} (x^{3} e^{y} + cos (y))

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{3} e^{y}) + \frac{\partial}{\partial x} (cos (y))

\frac{\partial}{\partial x} (x^{3} e^{y}) = 3 e^{y} x^{2}

\frac{\partial}{\partial x} (cos (y)) = 0

= 3 e^{y} x^{2} + 0

Simplify

= 3 e^{y} x^{2}

\int_{1}^{e^{2}} x^{2} ln (x) d x

\frac{x + 4}{x ^{3} + x - 5}

y = 2 x, x = 5, y = \frac{2}{x}

\int \frac{x + 1}{x ^{3} + x ^{2} - 6 x} d x

y = x^{2}, at x = - 0.5

What is (\partial)/(\partial x)(x^3e^y+cos(y)) ?
The answer to (\partial)/(\partial x)(x^3e^y+cos(y)) is 3e^yx^2