Second derivative using implicit differentiation with respect to x of x=siny+cosy 1=cosydydx−sinydydx 1=dydx(cosy−siny) dydx=1cosy−siny
Second derivative using implicit differentiation with respect to x of
Answer & Explanation
Take the derivative of both sides using one of the derivative rules:
Above are the beginnings to (i) the quotient rule and (ii) the power rule and chain rules.
Just differentiate both sides of with respect to x. This leads to:
first derivative by implicit diffferentiation; second derivetive subsitute the value of y' we hwve; simplifying this we have;