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If y=cos-1(cosx + 4sinx)/(17)1/2, then dy/dx is
- a)0
- b)1
- c)-1
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If y=cos-1(cosx + 4sinx)/(17)1/2, then dy/dx isa)0b)1c)-1d)None of the...
Solution:
Given, y = cos⁻¹(cosx 4sinx)/(17)1/2
Taking derivative of both sides w.r.t x,
dy/dx = d/dx [cos⁻¹(cosx 4sinx)/(17)1/2]
Let u = (cosx 4sinx)/(17)1/2
Then cos⁻¹u = y
Differentiating w.r.t x, we get
-1/(1 - u²) * du/dx = dy/dx
Now, we need to find du/dx
du/dx = d/dx [cosx 4sinx)/(17)1/2]
= -sinx/2(17)1/2 - 4cosx/2(17)1/2
= -(sinx + 4cosx)/(17)1/2
Substituting in the above equation,
dy/dx = -1/(1 - u²) * du/dx
= -1/(1 - (cosx + 4sinx)²/17) * (-(sinx + 4cosx)/(17)1/2)
= (sinx + 4cosx)/(17 - (cosx + 4sinx)²)1/2
Simplifying, we get
dy/dx = 1
Hence, the correct option is (B) 1.
Given, y = cos⁻¹(cosx 4sinx)/(17)1/2
Taking derivative of both sides w.r.t x,
dy/dx = d/dx [cos⁻¹(cosx 4sinx)/(17)1/2]
Let u = (cosx 4sinx)/(17)1/2
Then cos⁻¹u = y
Differentiating w.r.t x, we get
-1/(1 - u²) * du/dx = dy/dx
Now, we need to find du/dx
du/dx = d/dx [cosx 4sinx)/(17)1/2]
= -sinx/2(17)1/2 - 4cosx/2(17)1/2
= -(sinx + 4cosx)/(17)1/2
Substituting in the above equation,
dy/dx = -1/(1 - u²) * du/dx
= -1/(1 - (cosx + 4sinx)²/17) * (-(sinx + 4cosx)/(17)1/2)
= (sinx + 4cosx)/(17 - (cosx + 4sinx)²)1/2
Simplifying, we get
dy/dx = 1
Hence, the correct option is (B) 1.
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If y=cos-1(cosx + 4sinx)/(17)1/2, then dy/dx isa)0b)1c)-1d)None of theseCorrect answer is option 'B'. Can you explain this answer?
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