What is (\partial)/(\partial r)(rln(rs^2t^3)) ?

The answer to (\partial)/(\partial r)(rln(rs^2t^3)) is ln(rs^2t^3)+1

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(\partial)/(\partial r)(rln(rs^2t^3))

\frac{\partial}{\partial r} (r ln (r s^{2} t^{3}))

ln (r s^{2} t^{3}) + 1

Solution steps

\frac{\partial}{\partial r} (r ln (r s^{2} t^{3}))

Treat

s, t

as constants

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = r, g = ln (r s^{2} t^{3})

= \frac{\partial}{\partial r} (r) ln (r s^{2} t^{3}) + \frac{\partial}{\partial r} (ln (r s^{2} t^{3})) r

\frac{\partial}{\partial r} (r) = 1

\frac{\partial}{\partial r} (ln (r s^{2} t^{3})) = \frac{1}{r}

= 1 \cdot ln (r s^{2} t^{3}) + \frac{1}{r} r

Simplify

1 \cdot ln (r s^{2} t^{3}) + \frac{1}{r} r : ln (r s^{2} t^{3}) + 1

= ln (r s^{2} t^{3}) + 1

x \to + 1 lim (x (x - 2))

\frac{d}{d x} (sin (2 arcsin (x)))

x \to 0 lim (x - \frac{4}{x})

(2 y + 3 x) d x + x d y = 0

\int (2 + x^{6})^{8} 6 x^{5} d x

What is (\partial)/(\partial r)(rln(rs^2t^3)) ?
The answer to (\partial)/(\partial r)(rln(rs^2t^3)) is ln(rs^2t^3)+1