Q6 of 147 Page 183

Find the second order derivatives of the function
e^x sin 5x

Let us take y = e^x sin 5x

Now,

= e^xsin5x+e^xcos5x.5

= e^x (sin5x + 5cos5x)

= e^x (sin5x + 5cos5x) + e^x (5cos5x – 25sin5x)

= e^x (10cos5x – 24sin5x)

= 2e^x (5cos5x – 12sin5x)

Find the second order derivatives of the function

log x

Find the second order derivatives of the function

x³ log x

Find the second order derivatives of the function

e^6x cos 3x

Find the second order derivatives of the function

tan^–1 x

Find the second order derivatives of the functionex sin 5x