1/ f(x) = 5 sin(x) + ln(4x), find f '(x).

f '(x) =

2/ Use logarithmic differentiation to find the derivative of the function.

y = (x³ + 2)²(x⁵ + 4)⁴

y' =

3/ Use logarithmic differentiation to find the derivative of the function.

y = x^{4 cos(x)}

y' =

4/ Use a linear approximation (or differentials) to estimate the given number.

(1.999)⁵

5/ (a) Find the differential dy.

y = e^x/5

dy = ?

(b) Evaluate dy for the given values of x and dx.

x = 0,dx = 0.01

dy = ?

6/ Compute y and dy for the given values of x and dx = x.

y = x² 5x,x = 4,x = 0.5

y= dy=