What is (\partial)/(\partial x)(x^3+e^{y^2}) ?

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

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(\partial)/(\partial x)(x^3+e^{y^2})

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

3 x^{2}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (e^{y^{2}}) = 0

= 3 x^{2} + 0

Simplify

= 3 x^{2}

y^{^{'}} + y = sin (x)

x \to 5 lim (ln (\frac{x}{5}))

n = 1 \sum \infty n

f (x) = ln (4 x)

y^{^{''}} + y^{^{'}} + 5 y = 0, y (0) = 0, y^{^{'}} (0) = 0

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