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1. Diferentiate sqrt( sinx sin2x sin 3x)?2. Differentiate (x+5)^2. (x+4)^3. (x+5)^4?3. Differentiate( x^1/2(2x+3)^2)/(x+5)^3

1. Diferentiate sqrt( sinx sin2x sin 3x)?2. Differentiate (x+5)^2. (x+4)^3. (x+5)^4?3. Differentiate( x^1/2(2x+3)^2)/(x+5)^3

Grade:12th pass

1 Answers

Anusua
19 Points
3 years ago
Ans1)  Let u= sinx, v= sin2x and w= sin3x
            Using the formula, d(uvw)/dx= uv dw/dx+ vw du/dx+ wu dv/dx
                                              = (sinx)(sin2x) d(sin3x) + (sin2x)(sin3x) d(sinx)/dx+ (sinx)(sin3x) d(sin2x)/dx
                                              = (sinx)(sin2x)(3.cos3x) + (sin2x)(sin3x)(cosx) + (sinx)(sin3x)
Use the same formula for the second one
Ans 3) Let u= x^1/2, v= (2x+3)^1/2 and w= (x+5)^3
              d(uv/w)/dx= [w. d(uv)dx- (uv)dw/dx] / w^2
 

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