Question

differentiate log(2
$\sqrt{}$

Answer 1

Hey there,

Answer:

ddx[log2(x)]=1xln(2)

Explanation:

As we know how to differentiate ln(x) , we should change the base of the logarithm first.

The according formula to change a logarithmic expression from the base a to the base b is

loga(x)=logb(x)logb(a)

You can apply the formula as follows:

log2(x)=ln(x)ln(2)

As 1ln(2) is just a constant and the derivative of ln(x) is 1x , our derivative is:

ddx[log2(x)]=ddx[ln(x)ln(2)]=1ln(2)⋅1x=1xln(2)

Hope this helps!