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Let y=ln (1+ cos x)^(2). The the value o...

Let `y=ln (1+ cos x)^(2).` The the value of `(d^(2)y)/(dx^(2))+(2)/(e^(y//2))` equals

A

0

B

`(2)/(1+cos x)`

C

`(4)/(1+ cos x)`

D

`(-4)/(1+ cos x)^(2)`

Text Solution

AI Generated Solution

To solve the problem step by step, we start with the given function and find the second derivative, then combine it with the other term as required. ### Step 1: Define the function We start with the function: \[ y = \ln((1 + \cos x)^2) \] ### Step 2: Simplify using logarithmic properties Using the logarithmic property \( \ln(a^b) = b \ln(a) \): ...
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CENGAGE ENGLISH-DIFFERENTIATION-Execrises
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  2. "If "y^(1//m)=(x+sqrt(1+x^(2)))," then "(1+x^(2))y(2)+xy(1) is (where ...

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  3. If ( sin x) (cos y) = 1//2, then d^(2)y//dx^(2) at (pi//4, pi//4) is

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  4. A function f satisfies the condition f(x)=f'(x)+f''(x)+f'''(x)+…, wher...

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  5. Let f(x) be a polynomial of degree 3 such that f(3)=1, f'(3)=-1, f''(3...

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  6. If y^2=a x^2+b x+c , then y^3(d^2y)/(dx^2) is (a) a constant (b) a fun...

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  7. "If "y= sin x +e^(x)," then "(d^(2)x)/(dy^(2))=

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  8. If f''(x) =- f(x) and g(x) = f'(x) and F(x)=(f((x)/(2)))^(2)+(g((x)/(2...

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  9. Let y=ln (1+ cos x)^(2). The the value of (d^(2)y)/(dx^(2))+(2)/(e^(y/...

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  10. x=tcost ,y=t+sintdot Then (d^(2x))/(dy^2)a tt=pi/2 is (pi+4)/2 (b) -(p...

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  11. "Let "y=t^(10)+1 and x=t^(8)+1." Then "(d^(2)y)/(dx^(2)) is

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  12. If x = log p and y=(1)/(p), then

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  13. If x=varphi(t), y=psi(t),t h e n(d^(2y))/(dx^2) is (varphi^(prime)psi^...

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  14. If f(x)=x^4tan(x^3)-x1n(1+x^2), then the value of (d^4(f(x)))/(dx^4) ...

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  15. Let g(x) be the inverse of an invertible function f(x), which is diffe...

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  16. f(x)=e^(x)-e^(-x)-2 sin x -(2)/(3)x^(3). Then the least value of n for...

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  17. Let y=f(x) and x=(1)/(z)." If "(d^(2)y)/(dx^(2))=lamda(z^(3))(dy)/(dz)...

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  18. Let x=f(t) and y=g(t), where x and y are twice differentiable function...

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  19. If f(x) satisfies the relation f((5x-3y)/2)=(5f(x)-3f(y))/2AAx ,y in ...

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  20. A function f: R rarr R" satisfies sin x cos y "(f(2x+2y)-f(2x-2y))= co...

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