Implicit Differentiation
Background In some cases it is not possible to solve an equation as a single equation For Example: would be solved as two equations: and In order to find the derivative of the function, you would have had to find the derivative of each part
Implicit Differentiation Don’t need to solve an equation for y first in order to find y’ You will differentiate both sides with respect to x and solve the result for y’
Example Find y’ for
Practice Find y’ for:
Find the derivatives at the given points:
Find the equation of the tangent line to the function at the given point:
Find the second derivative 7) 8) 9)
Logarithmic Differentiation Derivatives of complicated functions can be simplified by taking logarithms
Example Find the derivative of