Question

Differentiation w. R. T "x" ​

Answer 1

y = log√x + √log x

diff. both sides w.r.t. x

dy/dy = ( log√x )' + ( √log x )'

here ' stands for differentiation

dy/dx = ( 1/log√x ) × ( √x )' + 1/(2 √ log x ) × ( log x )'

dy/dx = ( 1/log√x ) × 1/(2√x ) + 1/(2 √ log x ) × 1/x

Some Rules

• √ y w.r.t. x = 1/(2√y) × dy/dx

• log y w.r.t x = 1/log y × dy/dx