What is (\partial)/(\partial x)(2ln(x)+5ln(y)) ?

The answer to (\partial)/(\partial x)(2ln(x)+5ln(y)) is 2/x

Popular >

(\partial)/(\partial x)(2ln(x)+5ln(y))

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

\frac{2}{x}

Solution steps

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

Simplify

2 ln (x) + 5 ln (y) : ln (x^{2} y^{5})

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

Treat

y

as a constant

Apply the chain rule:

\frac{1}{x ^{2} y ^{5}} \frac{\partial}{\partial x} (x^{2} y^{5})

= \frac{1}{x ^{2} y ^{5}} \frac{\partial}{\partial x} (x^{2} y^{5})

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

= \frac{1}{x ^{2} y ^{5}} \cdot 2 y^{5} x

Simplify

\frac{1}{x ^{2} y ^{5}} \cdot 2 y^{5} x : \frac{2}{x}

= \frac{2}{x}

\int (5 x^{3} + 6 x) e^{x^{2}} d x

\int \frac{1}{9 y ^{2} + 4} d y

\int (1 - x) d x

e^{- 4 t} \times sin (2 t)

\frac{10}{3} x^{3} - 5 x^{2} - 11 x + 6

What is (\partial)/(\partial x)(2ln(x)+5ln(y)) ?
The answer to (\partial)/(\partial x)(2ln(x)+5ln(y)) is 2/x