# What is the derivative of #2^arcsin(x)#?

##### 1 Answer

Aug 3, 2016

#### Explanation:

Let:

#y=2^arcsin(x)#

Take the natural logarithm of both sides:

#ln(y)=ln(2^arcsin(x))#

Simplify using logarithm rules:

#ln(y)=arcsin(x)*ln(2)#

Differentiate both sides. You should remember that:

- The left-hand side will need the chain rule, similar to implicit differentiation.
- On the right-hand side,
#ln(2)# is just a constant. - The derivative of
#arcsin(x)# is#1/sqrt(1-x^2)# .

Differentiating yields:

#1/y*dy/dx=ln(2)/sqrt(1-x^2)#

Now, solving for

#dy/dx=(y*ln(2))/sqrt(1-x^2)#

Write

#dy/dx=(2^arcsin(x)ln(2))/sqrt(1-x^2)#