Exercise 10.2: Derivatives of basic elementary functions - Differentiation Rules

EXERCISE 10.2

Find the derivatives of the following functions with respect to corresponding independent variables:

(1) f(x) = x - 3 sinx

(2) y = sin x + cos x

(3) f(x) = x sin x

(4) y = cos x - 2 tan x

(5) g(t) = t3cos t

(6) g(t) = 4 sec t + tan t

(7) y = ex sin x

(8) y = tanx /x

(9) y = sin x / [1+ cos x]

(10) y = x / [sin x + cos x]

(11) y = tan x −1 / sec x

(12) y = sin x / x2

(13) y = tan θ(sin θ + cos θ)

(14) y = cosec x . cot x

(15) y = x sin x cos x

(16) y = e-x. log x

(17) y = (x2 +5) log(1+x)e-3x

(18) y = sin x°

(19) y = log10  x

(20) Draw the function f '(x) if f (x) = 2x2 − 5x + 3