Find the nth derivative of the following : eax+b - Mathematics and Statistics

प्रश्न

Find the n^th derivative of the following : e^ax+b

योग

उत्तर

Let y = e^ax+b

Then `"dy"/"dx" = "d"/"dx"(e^(ax + b))`

= `e^(ax + b)."d"/"dx"(ax + b)`

= `e^(ax + b) xx (a xx 1 + 0)`
= ae^ax+b

`(d^2y)/(dx^3) = "d"/"dx"(ae^(ax + b))`

= `a."d"/"dx"(ax + b)`

= `ae^(ax + b) xx (a xx 1 + 0)`
= a².e^ax+b

`(d^3y)/(dx^3) = "d"/"dx"[a^2e^(ax + b)]`

= `a^2"d"/"dx"(e^(ax + b))`

= `a^2e^(ax + b)."d"/"dx"(ax + b)`

= a²e^ax+b x (a x 1 + 0)
= a³.e^ax+bIn genaral, the nth order derivative is given by
`(d^ny)/(dx^n)` = aⁿ . e^ax+b.

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Derivatives of Implicit Functions

क्या इस प्रश्न या उत्तर में कोई त्रुटि है?

Q 4.03 Q 4.02 Q 4.04

अध्याय 1: Differentiation - Exercise 1.5 [पृष्ठ ६०]

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बालभारती Mathematics and Statistics 2 (Arts and Science) [English] 12 Standard HSC Maharashtra State Board

अध्याय 1 Differentiation
Exercise 1.5 | Q 4.03 | पृष्ठ ६०

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