1.

निम्न फलनों का अवकलन गुणांक ज्ञात कीजिए ` (i) sin 3x " "(ii) (4x+ 7)^(4) " "(iii) log (ax+ b ) `

Answer» माना `" "y=sin 3x,` माना 3x =t
अतः ` " "y=sin t `
`" " therefore " "(dy)/(dx) =(d )/(dx) sin t=(d)/(dt) sin t (dt)/(dx) `
` " "=cos t (d)/(dx) (3x) =3cos t `
` " " therefore (dy)/(dx) =3cos 3x `
(ii) माना ` y= (4x+7)^(4) , ` माना `4x+ 7=t `
अतः ` " "y= t^(4) `
` therefore (dy)/(dx) =(d)/(dx) t^(4) =(d)/(dt) t^(4)*(dt)/(dx) `
`" " =4t^(3) (d)/(dx) (4x+ 7) `
` " "=4t^(3) (4(d)/(dx) x+ (d)/(dx) 7) `
` " "=4t^(3) (4*1+0 )= 16t^(3)`
`therefore " "(dy)/(dx) =16 (4x+7 ) ^(3) `
,माना `y =log(ax+b) ` , माना `(ax+b) =t`
` "therefore " "(dy) /(dx) =(d)/(dx) log t =(d) /(dt) log t (d)/(dx) (ax+b ) `
` " "=(1)/(t) (a (d)/(dx) x+ (d) /(dx) b) =(a)/(t)=(a) /((ax+b) ) `
` therefore " "(dy)/(dx) =(a)/((ax+ b))`


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