What is (\partial)/(\partial x)(e^{z^2}+yln(x^2+5)) ?

The answer to (\partial)/(\partial x)(e^{z^2}+yln(x^2+5)) is (2yx)/(x^2+5)

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(\partial)/(\partial x)(e^{z^2}+yln(x^2+5))

\frac{\partial}{\partial x} (e^{z^{2}} + y ln (x^{2} + 5))

\frac{2 y x}{x ^{2} + 5}

Solution steps

\frac{\partial}{\partial x} (e^{z^{2}} + y ln (x^{2} + 5))

Treat

z, y

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (e^{z^{2}}) + \frac{\partial}{\partial x} (y ln (x^{2} + 5))

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

\frac{\partial}{\partial x} (y ln (x^{2} + 5)) = \frac{2 y x}{x ^{2} + 5}

= 0 + \frac{2 y x}{x ^{2} + 5}

Simplify

= \frac{2 y x}{x ^{2} + 5}

\frac{d y}{d x} = \frac{y}{x} + 2 x + 3

\frac{d y}{d t} = (y + 1) (y - 3), y (0) = 1

x \to \frac{4}{3} lim (2 x^{2} - 4 x + 5)

\int x (3^{- x^{2}}) d x

x \to 1 lim (1.7496)

What is (\partial)/(\partial x)(e^{z^2}+yln(x^2+5)) ?
The answer to (\partial)/(\partial x)(e^{z^2}+yln(x^2+5)) is (2yx)/(x^2+5)