Question

Solve y=p tan p + log(cos p) where p =dy/dx

Answer 1

Answer:

Here y=px + p2x Differentiating w.r.t. x, we get dy dx = p + x 2 2 dp dp Solution: y = p tan p + log cosp

Step-by-step explanation:

May this ANSWER will help you plz mark has brainliest

Answer 2

Given : y = ptanp + log(cosp) where p = dy/dx

To find : x in terms of p

Solution:

y = ptanp + log(cosp)

p = dy/dx

y = ptanp + log(cosp)

differentiating wrt x

=> dy/dx  = p sec²p (dp/dx)  + tanp (dp/dx)  +  (1/Cosp)(-Sinp)(dp/dx)

=> dy/dx  = p sec²p (dp/dx)  + tanp (dp/dx)  - tanp(dp/dx)

=> dy/dx  = p sec²p (dp/dx)

dy/dx = p

=> p = p sec²p (dp/dx)

=> 1 = sec²p (dp/dx)

=> dx = sec²p (dp)

integrating both sides

=> x  = tanp + c

Learn more:

Integration of x²×sec²(x³) dx - Brainly.in

brainly.in/question/18063473

brainly.in/question/19073214

https://brainly.in/question/19205476