Question

Differentiation of Trigonometric, Logarithmic & Exponential function.?

y = cos^2 (2x^2 + 5)

y = e^(3x) – e^(2-x)

y = ln (3x2 + x)

Answer

a)

y = cos^2 [2x^2 + 5 ]

y ' = 2 cos (2x^2 + 5)*( - sin (2x^2 + 5)* (4x)

= -8x cos (2x^2 + 5) sin(2x^2 + 5)

= -4x sin [4x^2 + 10 ] ( since sin(2x) = 2sin x cos x )

b)

y = e^(3x) - e^(2 - x)

y ' = 3e^(3x) - e^(2 - x)(-1)

= 3e^(3x) + e^(2 - x)

c)

y = ln (3x^2 + x)

y ' = (6x + 1) / (3x^2 + x)

Aug 23 at 6:49

1)-2cos(2x^2 + 5) sin ( 2x^2 + 5) (4x)

2) 3e^(3x) + e ^ (2 -x)

3) 6x +1 / 3x^2 +x

Aug 23 at 10:35