What is (\partial)/(\partial x)(log_{10}(x+y)) ?

The answer to (\partial)/(\partial x)(log_{10}(x+y)) is 1/(ln(10)(x+y))

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(\partial)/(\partial x)(log_{10}(x+y))

\frac{\partial}{\partial x} (lo g_{10} (x + y))

\frac{1}{ln ( 10 ) ( x + y )}

Solution steps

\frac{\partial}{\partial x} (lo g_{10} (x + y))

Treat

y

as a constant

Apply log rule:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{\partial}{\partial x} (\frac{ln ( x + y )}{ln ( 10 )})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{ln ( 10 )} \frac{\partial}{\partial x} (ln (x + y))

Apply the chain rule:

\frac{1}{x + y} \frac{\partial}{\partial x} (x + y)

= \frac{1}{x + y} \frac{\partial}{\partial x} (x + y)

\frac{\partial}{\partial x} (x + y) = 1

= \frac{1}{ln ( 10 )} \cdot \frac{1}{x + y} \cdot 1

Simplify

\frac{1}{ln ( 10 )} \cdot \frac{1}{x + y} \cdot 1 : \frac{1}{ln ( 10 ) ( x + y )}

= \frac{1}{ln ( 10 ) ( x + y )}

\int t sin (9 t) d t

(2.3) (4.4)

\frac{\partial}{\partial y} (4 y x)

x \to 3 lim (\frac{2}{x ^{2} - 9})

y = x, 4 x + y^{2} = 12

What is (\partial)/(\partial x)(log_{10}(x+y)) ?
The answer to (\partial)/(\partial x)(log_{10}(x+y)) is 1/(ln(10)(x+y))