Question

f(x) = x - + 5x -4 b) f(x) = x'senx COS X f (x) 1-senx d) f(x) = xe" -5e" e) F(x)= In 3

derivated the following exercises

Answer 1

SOLUTION :

a.

f(x) = x^2 - 2/x + 5x - 4

 f’ (x) 

= 2x - 2(-1)/x^2 + 5 

= 2x + 2/x^2 + 5 (ANSWER).

b.

f(x) = x^3 sen x  , I think it is x^3 sin x 

Accordingly,

f’ (x)

= x^3 d/dx (sin x) + d/dx (x^3) sin x

= x^3 cos x + 3x^2 sin x (ANSWER).

c.

f(x) = cos x / (1 - sin x) 

f’ (x) 

= cos x d/dx (1 - sin x)^(-1) + d/dx (cos x) / (1 - sin x)

= - cos x / (1 - sin x)^2 * (- cos x) + (- sin x) / (1 - sin x)

= cos^2 x / (1 - sin x)^2 - sin x / (1 - sin x)

= [ cos^2 x - sin x (1 - sin x) ] / (1 - sin x)^2

= [ cos^2 x - sin x + sin^2 x ] / (1 - sin x)^2

= (1 - sin x) / (1 - sin x)^2

= 1 / (1 - sin x) (ANSWER).

d. 

f(x) = xe^x - 5e^x 

f’ (x)

= xe^x + e^x - 5e^x

= xe^x - 4e^x (ANSWER).

e.

f(x) = ln(5/x) = ln(5) - ln(x)

f’ (x)

= 0 - 1/x 

= - 1/x  (ANSWER).

Answer 2

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