Current Location  >  Math Formulas > Calculus > Derivatives of Exponential and Logarithmic Functions

Derivatives of Exponential and Logarithmic Functions

ax

ax ∙ lna, where a is a constant

ex

ex

ec∙x

c∙ec∙x, where c is a constant

xx

xx(1+ln(x))

log(x), where the base is 10

1/(x∙ln(10))

loga(x), where the base is a

1/(x∙ln(a))

ln(x)

1/x

f g, f and g are both functions

f g(g '∙ln(f)+(g/f)∙f ')


Example 1: Find the derivative of f(x) = ln(tan x).

 

f´(x) = 1 / tan(x) * d/dx * tan(x)

 

f´(x) = 1 / tan(x) * sec2(x)

 

 

Example 2: Find the derivative of f(x) = e(2x-1)

 

f´(x) = e(2x-1) * d(2x -1 ) / dx

 

f´(x) = e(2x-1) * 2

 

 

Example 3: Find d(3x) / dx

 

d(3x) / dx = 3xln3

 

Example 4: Find the derivative of xx-2

Let y =xx-2

 

Take natural logarithm on both the sides

lny = (x-2)lnx

 

We now differentiate both sides with respect to x, using chain rule on the left side and the product rule on the right.




Multiply y on the right hand side

 

dy/dx = y [lnx*1 + (x-2)/x]

 

dy/dx = xx-2[lnx*1 + (x-2)/x]

 

dy/dx =xx-3(x*lnx + x – 2)



Web-Formulas.com © 2017 | Contact us | Terms of Use | Privacy Policy | Yellow Sparks Network
Web Formulas