Calculus: Differentation

 Let’s we talk about Calculus especially about Differential. Start from easy, let’s see this function:

1.       F(x) = 4x⁴ + 5x³ + 6x + 7

This function after differential becomes:

dx/dy F(x) = dx/dy 4x⁴ + 5x³ + 6x + 7

                      = 16x³ + 15x² + 6

What about if F(x) = 2^x, it’s very difficult for us. So we need to us natural logarithm (ln), let’s see how it’s work!

F(x) = 2^x, suppose that F(x) = y so that,

y = 2^x

ln y = ln 2^x

ln y = x ln 2

dy/dx ln y = dy/dx x ln 2

1/y = dy/dx ln 2

è dx/dy = y ln 2

            = 2^x (ln 2)

So, we conclude that if F(x) = a^x, the differential will be a^x (ln a)

Thank you everybody  J