Question

3
Find d^2y/dx^2, if y = x^3+
tanx​

Answer 1

Answer:

6x + 2sec²x.tanx

Step-by-step explanation:

dy/dx = d(x³ + tanx)/dx

= dx³/dx + dtanx/dx

= 3x² + sec²x

Further,

d²y/dx² = d(3x² + sec²x)/dx

= d(3x²)/dx + d(sec²x)/dx

= 3(2)x + 2sec²x.tanx

= 6x + 2tanx.sec²x

for differentiating sec²x wrt x:

=> d(sec²x)/dx , let secx = t,

=> d(t²)/dx

=> d(t²)/dt * dt/dx

=> 2t * dt/dx

=> 2(secx) * d(secx)/dx

=> 2secx * secx.tanx

=> 2sec²xtanx