Types of differentiation

Explicit Differentiation vs Implicit Differentiation
Written by: Jack Methew

Jack Methew knows that successful students become successful adults. This is her 15th year at Edison Elementary School and her 10th year teaching fourth grade. So far, fourth grade is her favorite grade to teach! Mrs. Carroll was the 2011 Newell Unified School District Teacher of the Year, and received her National Board Certification in 2013. She loves science and majored in biology at Arizona State University, where she also earned her teaching credential and Master of Education degree. Mrs. Carroll is excited to begin the best year ever!

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Explicit Differentiation vs Implicit Differentiation

Explicit Differentiation:

As we have discussed before,explicit function when we write y as function of “x”

Example

$$y=x^2$$

$$\text{Let}\;y=x^2+sinx$$

Fact:Here there is no y which means that explicit differentiation

$$y’=2x+cosx$$

Implicit Differentiation:

When y cannot be written as function of “x”

Example

$$xy=8$$

$$xy’+y(1)=0$$

$$xy’+y$$

By use of product rule(fg’+gf’)

$$\frac{dy}{dx}=\frac{-y}{x}$$