What is the derivative of f(x)=sqrt(log_{a)(x)} ?

The derivative of f(x)=sqrt(log_{a)(x)} is 1/(2xln(a)sqrt(log_{a)(x))}

What is the first derivative of f(x)=sqrt(log_{a)(x)} ?

The first derivative of f(x)=sqrt(log_{a)(x)} is 1/(2xln(a)sqrt(log_{a)(x))}

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derivative of

f (x) = lo g_{a} (x)

\frac{1}{2 x ln ( a ) lo g _{a} ( x )}

Solution steps

\frac{d}{d x} (lo g_{a} (x))

Apply the chain rule:

\frac{1}{2 lo g _{a} ( x )} \frac{d}{d x} (lo g_{a} (x))

= \frac{1}{2 lo g _{a} ( x )} \frac{d}{d x} (lo g_{a} (x))

\frac{d}{d x} (lo g_{a} (x)) = \frac{1}{x ln ( a )}

= \frac{1}{2 lo g _{a} ( x )} \cdot \frac{1}{x ln ( a )}

Simplify

\frac{1}{2 lo g _{a} ( x )} \cdot \frac{1}{x ln ( a )} : \frac{1}{2 x ln ( a ) lo g _{a} ( x )}

= \frac{1}{2 x ln ( a ) lo g _{a} ( x )}

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

y = 4 e^{x}

\frac{\partial}{\partial t} (t^{2})

x \to 0 lim (arctan (6 x))

x \to - 3 lim (5 - x)

What is the derivative of f(x)=sqrt(log_{a)(x)} ?
The derivative of f(x)=sqrt(log_{a)(x)} is 1/(2xln(a)sqrt(log_{a)(x))}
What is the first derivative of f(x)=sqrt(log_{a)(x)} ?
The first derivative of f(x)=sqrt(log_{a)(x)} is 1/(2xln(a)sqrt(log_{a)(x))}