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

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

A

`(-sin x +e^(x))^(-1)`

B

`(sin x - e^(x))/((cos x +e^(x))^(2))`

C

`(sin x - e^(x))/((cos x +e^(x))^(3))`

D

`(sin x + e^(x))/((cos x +e^(x))^(3))`

Text Solution

AI Generated Solution

To solve the problem, we need to find \(\frac{d^2x}{dy^2}\) given that \(y = \sin x + e^x\). ### Step-by-Step Solution: 1. **Write the given equation:** \[ y = \sin x + e^x \] ...
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CENGAGE ENGLISH-DIFFERENTIATION-Execrises
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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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