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Find the second order derivative of the function. e^6x cos 3x

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प्रश्न

Find the second order derivative of the function.

e6x cos 3x

योग
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उत्तर

Let, y = e6x cos 3x

Differentiating both sides with respect to x,

`dy/dx = e^(6x) d/dx cos 3 x + cos 3 x d/dx e^(6x)`

= `e^(6x) (- sin 3 x) d/dx (3x) + cos 3 x * e^(6x) d/dx (6x)`

= −3e6x sin 3x + 6e6x cos 3x

= e6x (6 cos 3x − 3 sin 3x)

Differentiating both sides again with respect to x,

`(d^2 y)/dx^2 = e^(6x) d/dx (6 cos 3 x - 3 sin 3 x) + (6 cos 3 x - 3 sin 3 x) d/dx e^(6x)`

= `e^(6x) [6 (- sin 3x) d/dx (3x) - 3 cos 3x d/dx (3x)] + [6 cos 3x - 3 sin 3x]e^(6x) d/dx (6x)`

= e6x [−6 sin 3x · 3 − 3 cos 3x · 3] + [6 cos 3x − 3 sin 3x] × e6x ⋅ 6

= e6x [−18 sin 3x − 9 cos 3x] + e6x [36 cos 3x − 18 sin 3x]

= e6x [−36 sin 3x + 27 cos 3x]

= 9e6x [3 cos 3x − 4 sin 3x]

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  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 5: Continuity and Differentiability - Exercise 5.7 [पृष्ठ १८३]

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एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
अध्याय 5 Continuity and Differentiability
Exercise 5.7 | Q 7 | पृष्ठ १८३

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