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Find differentiation of y w.r.t x. (i) y...

Find differentiation of y w.r.t x. (i) `y=(sin x)/x` , (ii) `y=(4x^(3))/e^(x)`

Text Solution

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(i) Here `f(x)=sinx, g(x)=x` So, `f'(x)=cos x, g'(x)=1`
Therefore `(dy)/(dx)=((cos x)(x)-(sin x)(1))/x^(2)=(x cos x-sin x)/x^(2)`
(ii) Here `f(x)=4x^(3), g(x)=e^(x)` So `f'(x)=12x^(2), g'(x)=e^(x)`
Therefore, `(dy)/(dx)=(12x^(2)(e^(x))-4x^(3)(e^(x)))/((e^(x))^(2))=(12x^(2)-4x^(3))/e^(x)`
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