# Implicit Differentiation

Implicit differentiation is a fundamental technique in calculus used to find the derivatives of functions that are not expressed explicitly. It is particularly useful when dealing with equations that are not in the form y = f(x) but rather involve both x and y variables. By applying the chain rule, implicit differentiation allows us to compute derivatives efficiently without having to isolate y explicitly. This method plays a crucial role in various branches of mathematics and physics, enabling the analysis of curves and surfaces defined implicitly by equations, providing insights into their behavior and characteristics.

Questions

- What is the implicit derivative of #1= x^2y-e^y-xy #?
- How do you differentiate #-2=yln(e^(x-y^3))+xe^(x-y)#?
- How do you find #(dy)/(dx)# given #x^3+y^4=0#?
- How do you differentiate #1=e^(xy)/(e^x+e^y)#?
- How do you implicitly differentiate #-y= x^3y^2-3x^2y^3-7xy^4 #?
- How do you differentiate #-2y=x-cosy/(xy)#?
- How do you differentiate #tan 2x = cos 3y#?
- How do you implicitly differentiate # sqrt(3x+3y) + sqrt(3xy) = 17.5#?
- What is the derivative of #x^(2/3)+y^(2/3)=5# at the given point of #(8,1)#?
- How do you implicitly differentiate #2=(x+2y)^2-xy-e^(3x+y^2) #?
- How do you implicitly differentiate #4= xytan(x^2y) #?
- How do you differentiate #y=x^2y-y^2x#?
- How do you implicitly differentiate #7=1-e^y/(xy)#?
- How do you use implicit differentiation to find #(dy)/(dx)# given #sqrtx+sqrty=1#?
- How do you implicitly differentiate #-1=(x+y)^2-xy-e^(3x+7y) #?
- How do you implicitly differentiate # y^2+(y-x)^2-y/x^2-3y#?
- How do you find the derivative of #arctan(x^2y)#?
- How do you find the derivative of y in the equation #ln(xy)=x+y#?
- How do you differentiate #ycosx^2-y^2=xy#?
- How do you differentiate #y=(x-y)^2/(x+y)#?