DHomework1. Find the derivative of = 2. Differentiate y = [tan3. Integrate 4. Evaluate 5. Use...

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DHomework1. Find the derivative of = 2. Differentiate y = [tan3. Integrate 4. Evaluate 5. Use Logarithmic differentiation to find the derivative of y = 6. Use Logarithmic differentiation to find the derivative of y = xn7. Write as a single logarithm8. Integrate 9. Integrate 10. Integrate 11. Integrate 12. Integrate 13. Integrate 14. Integrate 15. Find the derivative of y = 16. Find the derivative of y = 17. Find 18. Compute the derivative of cos-1(3)19. Find the derivative of f(x) = sinh2(3x)20. Integrate 
	
Document Preview: DHomework1.   Find the derivative of  f(x) = log2+sin2x2.   Differentiate   y = ln[tan(e5x)]3.    Integrate    2x(x+1)2dx4.  Evaluate   0p41+tan2x dx5. Use Logarithmic differentiation to find the derivative of   y = xx6.  Use Logarithmic differentiation to find the derivative of   y = xn7.  Write as a single logarithm                      XXXXXXXXXX32lnx2+1-ln(x+1)-ln(x-1)8.   Integrate   2sinxcosxdx9.     Integrate    dxxlogx10.   Integrate  (x-1x)2dx11.   Integrate  (xp-px)dx12.  Integrate  (x6-1x2-1)dx13.   Integrate  sin2xcosx dx XXXXXXXXXXIntegrate    ex-e-xex+e-xdx15.    Find the derivative of  y = ln1+ex1-ex16.   Find the derivative of  y = xx-117.    Find xx4+9  dx18.    Compute the derivative of  cos-1(3x2)19.    Find the derivative of f(x) = sinh2(3x) XXXXXXXXXXIntegrate  cosh2x dx

Robert · Accepted Answer

D
Homework
1. Find the derivative of   = 
Ans: 
f(x) = log√(2+sin2x) = ln√(2+sin2x) /ln 10
f’(x) = [1/√(2+sin2x)][1/2√(2+sin2x)][2sin x cos x]/ln 10 = sin 2x/(2+sin2x)ln 10
2. Differentiate   y = [tan
Ans: 
f’(x) = [1/tan(e5x)][sec2(e5x)][5e5x] = 5e5x /sin(e5x) cos (e5x) = 5e5x/sin(2e5x)
3. Integrate  
Ans: 
Let x+1 = t
·  dx = dt
I = ∫2(t – 1)/t2dt = 2∫(1/t – 1/t2)dt = 2(ln t + 1/t) + c = 2[ln(x+1) + 1/(x+1)] + c 
4. Evaluate    
√(1 + tan2x) = √sec2x = sec x
0∫π/4 sec x = ln |sec x + tan x|0π/4 = ln (√2 + 1)
5.

D Homework 1. Find the derivative of = 2. Differentiate y = [tan 3. Integrate 4. Evaluate 5. Use Logarithmic differentiation to find the derivative of y = 6. Use Logarithmic differentiation to find...

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