Use implicit differentiation to find dy/dx .

Question

Use implicit differentiation to find dy/dx .

ln(y) − 4x ln(x) = −8

Answer 1

Given equation ln (y) - 4x ln(x) = -8 differentiating both sides w.r.t. x

we get 1/y dy/dx - 4x/x - 4 ln(x) = 0 simpl;ify

1/y dy/dx = 4 + 4 ln(x)

dy/dx = 4 y (1+ ln(x) )

I hope this answer make sense to you.

Shailesh (Sky) Kadakia

Answer 2

ln(y) − 4x ln(x) = −8

ln(y) = 4x ln(x) −8

y= e^{4x ln(x) -8}

dy/dx= d(4x ln(x) −8) * e^{4x ln(x) -8}

d(4x ln(x) −8)= 4ln(x) +(1/x)*4x= 4ln(x) +4 = 4(ln(x)+1)

so dy/dx= 4(ln(x)+1) e^{4x ln(x) -8}

^{i hope it is clear}