Aim: How do we calculate more complicated derivatives?

Simple Derivatives Calculate the following derivates: f(x) =4x6 df/dx=24x3 f(x) = 3x2 df/dx=6x What general rule are we using? If f(x)=kxn , df/x=nkxn-1

Common Derivatives in the Reference Table df/dx = df/du * du/dx d/dx (xn ) = nxn-1 d/dx (ex) = ex d/dx (lnx) = 1/x d/dx (sinx) = cosx d/dx (cosx) = -sinx

More complicated derivatives to solve: How would we find the derivative of this function? f(x) = sin (7x)

Example Solved Use the concept that df/dx = df/du * (du/dx) to find derivative of f(x) = (sin 7x) (Let u = 7x) If f(x) = sin7x, then f(u) = sin (u) df/du = cos (u) and du/dx = 7 Thus, df/dx = 7 *sin(7x)

Solve for the following derivatives f(x) = cos (4x) df/dx=-4sin(4x) f(x) = sin (6x2) df/dx=12xcos(6x2) f(x) = 13 ln (5x) df/dx=13/x f(x) = ln(4x3 ) df/dx=3/x f(x) = 25/ 1 –x2 df/dx=50x/(1-x2)2 f(x) = e4x df/dx=4e4x

7) f(x) =sin(11x) df/dx=11cos(11x) 8) f(x) = sin (11x3 ) df/dx=33x2 cos(11x3) 9) f(x) = 6/(1- 20x) df/dx=120/(1-20x)2 10) f(x) = e2x df/dx=2e2x 11) f(x) =5 ln (2x2 ) df/dx=10/x 12) f(x) = e3x^2 df/dx=6xe3x^2