What is (\partial)/(\partial t)(ln(x+t^2)) ?

The answer to (\partial)/(\partial t)(ln(x+t^2)) is (2t)/(x+t^2)

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(\partial)/(\partial t)(ln(x+t^2))

\frac{\partial}{\partial t} (ln (x + t^{2}))

\frac{2 t}{x + t ^{2}}

Solution steps

\frac{\partial}{\partial t} (ln (x + t^{2}))

Treat

x

as a constant

Apply the chain rule:

\frac{1}{x + t ^{2}} \frac{\partial}{\partial t} (x + t^{2})

= \frac{1}{x + t ^{2}} \frac{\partial}{\partial t} (x + t^{2})

\frac{\partial}{\partial t} (x + t^{2}) = 2 t

= \frac{1}{x + t ^{2}} \cdot 2 t

Simplify

\frac{1}{x + t ^{2}} \cdot 2 t : \frac{2 t}{x + t ^{2}}

= \frac{2 t}{x + t ^{2}}

\frac{d}{d x} (\frac{7 + 8 x - 4 x}{x})

\int \frac{484 - x ^{2}}{x} d x

a re a x^{3}, x + 6 = y, \frac{- x}{2} = y

\frac{\partial}{\partial y} (ln (x y))

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

What is (\partial)/(\partial t)(ln(x+t^2)) ?
The answer to (\partial)/(\partial t)(ln(x+t^2)) is (2t)/(x+t^2)