How do you differentiate #f(x)=e^(cossqrtx)# using the chain rule.?

1 Answer
Jun 21, 2016

Answer:

#e^cos(sqrt(x)) xx (-sin(sqrt(x))) xx 1/(2sqrt(x))#

Explanation:

Understand this that this is in the form of #f(g(h(x)))# where #f(x) = e^x#, #g(x)=cos(x)# and #h(x) = sqrt(x)#

First, you need to know these things

#d/dx(e^x)=e^x#
#d/dx(cos(x))=-sin(x)#
#d/dx(sqrt(x))=1/(2sqrt(x))#

So, this becomes

Derivative = #e^cos(sqrt(x)) xx (-sin(sqrt(x))) xx 1/(2sqrt(x))#