Find dydxdydx, if : x = a2+m2,y=log(a2+m2) - Mathematics and Statistics

प्रश्न

Find `"dy"/"dx"`, if : x = `sqrt(a^2 + m^2), y = log(a^2 + m^2)`

योग

उत्तर

x = `sqrt(a^2 + m^2), y = log(a^2 + m^2)`
Differentiating x and y w.r.t. x, we get
`"dx"/"dm" = "d"/"dm"(sqrt(a^2 + m^2))`

= `(1)/(2sqrt(a^2 + m^2))."d"/"dm"(a^2 + m^2)`

= `(1)/(2sqrt(a^2 + m^2)) xx (0 + 2m) = m/sqrt(a^2 + m^2)`
and
`"dy"/"dm" = "d"/"dm"[log(a^2 + m^2)]`

= `(1)/(a^2 + m^2)."d"/"dm"(a^2 + m^2)`

= `(1)/(a^2 + m^2) xx (0 + 2m) = (2m)/(a^2 + m^2)`

∴ `"dy"/"dx" = (("dy"/"dm"))/(("dx"/"dm"))`

= `(((2m)/(a^2 + m^2)))/((m/sqrt(a^2 + m^2))`

= `(2)/sqrt(a^2 + m^2)`.

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Derivatives of Implicit Functions

क्या इस प्रश्न या उत्तर में कोई त्रुटि है?

Q 1.3 Q 1.2 Q 1.4

अध्याय 1: Differentiation - Exercise 1.4 [पृष्ठ ४८]

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

अध्याय 1 Differentiation
Exercise 1.4 | Q 1.3 | पृष्ठ ४८

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