What is (\partial)/(\partial θ)(nln(2θ)) ?

The answer to (\partial)/(\partial θ)(nln(2θ)) is n/θ

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(\partial)/(\partial θ)(nln(2θ))

\frac{\partial}{\partial θ} (n ln (2 θ))

\frac{n}{θ}

Solution steps

\frac{\partial}{\partial θ} (n ln (2 θ))

Take the constant out:

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

= n \frac{\partial}{\partial θ} (ln (2 θ))

Apply the chain rule:

\frac{1}{2 θ} \frac{\partial}{\partial θ} (2 θ)

= \frac{1}{2 θ} \frac{\partial}{\partial θ} (2 θ)

\frac{\partial}{\partial θ} (2 θ) = 2

= n \frac{1}{2 θ} \cdot 2

Simplify

n \frac{1}{2 θ} \cdot 2 : \frac{n}{θ}

= \frac{n}{θ}

\int \frac{50 x}{sec ( 5 x ^{2} + 5 )} d x

x \to 0 lim (\frac{( 8 ^{x} - 5 ^{x} )}{x})

\frac{1}{e ^{x^{2}}}

y^{^{'}} = x y^{3} - x y

x^{5} - x^{3} + x, 1

What is (\partial)/(\partial θ)(nln(2θ)) ?
The answer to (\partial)/(\partial θ)(nln(2θ)) is n/θ