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Differentiation help!

May sound silly question, but trying to teach myself... can someone help me with finding the derivatives of the following equations:

e^x/2

Ln(x/4)

Find the gradient of the curve whose equation is y=e^3x at the point (0,1)

Reply 1

MartyO

You should look into chain derivatives for compositions of functions. Otherwise, you have to rely upon a table of derivatives for the derivative of the natural logarithm.
If you ever need examples of full solutions to derivatives, you should try out this derivative calculator with steps.

(edited 7 years ago)

Reply 2

NotNotBatman

Original post by Olmeister

Use the chain rule.

Reply 3

asinghj

As people above me said, use the chain rule... for the ln(x/4) though I would use one of the log rules first

Reply 4

Kawaii289

Original post by asinghj

As people above me said, use the chain rule... for the ln(x/4) though I would use one of the log rules first

We want dy/dx
y=ln(x/4)
let u = x/4
du/dx = 1/4
...
y=ln(u)
dy/du = 1/u
1/u = 4/x

therefore dy/du *du/dx = dy/dx (in this case behaves like a fraction and du cancels)
so 4/x * 1/4 = 1/x
dy/dx = 1/x

(edited 7 years ago)

Reply 5

asinghj

Original post by Kawaii289

We want dy/dx
y=ln(x/4)
let u = x/4
du/dx = 1/4
...
y=ln(u)
dy/du = 1/u
1/u = 4/x

therefore dy/du *du/dx = dy/dx (in this case behaves like a fraction and du cancels)
so 4/x * 1/4 = 1/x
dy/dx = 1/x