sin (x^(2) + 5)...

`sin (x^(2) + 5)`

Text Solution

AI Generated Solution

To differentiate the function \( y = \sin(x^2 + 5) \) with respect to \( x \), we will use the chain rule. Here’s a step-by-step solution: ### Step 1: Identify the outer and inner functions We have: - Outer function: \( \sin(u) \) where \( u = x^2 + 5 \) - Inner function: \( u = x^2 + 5 \) ### Step 2: Differentiate the outer function ...

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If y=sin (x^(2) +x+5) ,then (dy)/(dx) =

` -(x+1) cos(x^(2) +x+ 5)`

` (x+1) cos (x^(2) +x+5)`

` -(2x+1) cos ( x^(2) +x+5) `

` (2x +1)cos (x^(2) +x+5) `

If y=cos (x^(3)) sin ^(2) (x^(5)),then (dy)/(dx) =

` 5x^(4)sin (x^(3))sin (2x^(5))-3x^(2) cos (x^(3))sin ( x^(5))`

` 5x^(4)sin (x^(3))sin (2x^(5))+ 3x^(2) cos (x^(3))sin ( x^(5))`

` 5x^(4)sin (x^(3))sin (2x^(5))- 3x^(2) sin (x^(3))sin^(2) ( x^(5))`

` 5x^(4)sin (x^(3))sin (2x^(5))+ 3x^(2) sin (x^(3))sin^(2) ( x^(5))`

int_(0)^(pi//2) (dx)/(4sin^(2) x + 5 cos^(2)x)

`(pi)/(2sqrt(5))`

`pi/4`

`(pi)/(4sqrt(5))`

`(pi)/sqrt(5)`