Can someone please explain this?

This is from an online site. What I don't understand is where #1/ydy/dx# has come from. This is as on the site.

#y=1.3^x=>lny=ln1.3^x=>lny=xln1.3#

#=>1/ydy/dx=ln1.3=>dy/dx=yln1.3#

#=>dy/dx=1.3^xln1.3#

1 Answer
Jan 7, 2018

See below.

Explanation:

Starting from:

#lny=xln1.3#

If we differentiate this implicitly, we use the chain rule. When differentiating #lny#, we differentiate #y# in respect of #y# multiplied by #y# in respect of #x#.

#:.#

#(df(y))/dx=(df(y))/dy*dy/dx#

So:

#f(y)=lny#

#lny=xln1.3#

#(df(y))/dy(lny)*dy/dx= ln(1.3)dy/dxx#

#1/y*dy/dx= ln(1.3)=>dy/dx=yln1.3#

#y=1.3^x=>dy/dx=1.3^xln1.3#