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If y = [f(x)g(x)h(x)lmnabc], prove that dydx =|f′(x)g′(x)h′(x)lmnabc| - Mathematics

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प्रश्न

if y = `[(f(x), g(x), h(x)),(l, m,n),(a,b,c)]`, prove that `dy/dx` =`|(f'(x), g'(x), h'(x)),(l,m, n),(a,b,c)|`

योग

उत्तर

y = `|(f(x), g(x), h(x)),(l, m, n),(a, b, c)|`

`dy/dx= |(d/dx (f(x)), d/dx (g(x)), d/dx (h(x))), (l, m , n), (a, b, c)|`

` + |(f(x), g(x), h(x)),(0, 0, 0),(a, b, c)| + |(f(x), g(x), h(x)),(l, m, n),(0, 0, 0)|`

`= |(f'(x), g'(x), h'(x)),(l, m, n),(a, b, c)|`

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अध्याय 5: Continuity and Differentiability - Exercise 5.9 [पृष्ठ १९२]

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एनसीईआरटी Mathematics [English] Class 12
अध्याय 5 Continuity and Differentiability
Exercise 5.9 | Q 22 | पृष्ठ १९२

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