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प्रश्न
Select the correct answer from the given alternative:
If y = `(5sin x - 2)/(4sin x + 3)`, then `("d"y)/("d"x)` =
विकल्प
`(7 cos x)/(4 sin x + 3)^2`
`(23 cos x)/(4 sin x + 3)^2`
`- (7 cos x)/(4 sin x + 3)^2`
`-(15 cos x)/(4 sin x + 3)^2`
उत्तर
If y = `(5sin x - 2)/(4sin x + 3)`, then `("d"y)/("d"x)` = `underline ((23 cos x)/(4 sin x + 3)^2)`
Explanation:
y = `(5sinx - 2)/(4 sin x + 3)`
Differentiating w.r.t.x, we get
`(dy)/(dx) = ((4sinx + 3)d/dx(5sinx - 2) - (5sinx - 2)d/dx (4sinx + 3))/(4sinx + 3)^2`
= `((4sin x + 3)(5cosx) - (5sinx - 2)(4cos x))/(4 sinx + 3)^2`
= `(20sin x cosx + 15cosx - 20sinxcosx + 8cosx)/(4sinx + 3)^2`
= `(23cosx)/(4sinx + 3)^2`
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y = `sinx logx + "e"^x cos x - "e"^x sqrt(x)`
Differentiate the following w.r.t.x. :
y = `"e"^x tanx + cos x log x - sqrt(x) 5^x`
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y = `(x^2 sin x)/(x + cos x)`
Fill in the blanks:
y = ex .tan x
Differentiating w.r.t.x
`("d"y)/("d"x) = "d"/("d"x)("e"^x tan x)`
= `square "d"/("d"x) tanx + tan x "d"/("d"x) square`
= `square square + tan x square`
= `"e"^x [square + square]`
Fill in the blanks:
y = `sinx/(x^2 + 2)`
Differentiating. w.r.t.x.
`("d"y)/("d"x) = (square "d"/("d"x) (sin x) - sin x "d"/("dx) square)/(x^2 + 2)^2`
= `(square square - sin x square)/(x^2 + 2)^2`
= `(square - square)/(x^2 + 2)^2`
Fill in the blanks:
y = (3x2 + 5) cos x
Differentiating w.r.t.x
`("d"y)/("d"x) = "d"/("d"x) [(3x^2 + 5) cos x]`
= `(3x^2 + 5) "d"/("d"x) [square] + cos x "d"/("d"x) [square]`
= `(3x^2 + 5) [square] + cos x [square]`
∴ `(dx)/("d"y) = (3x^2 + 5) [square] + [square] cos x`
Fill in the blank:
Differentiate tan x and sec x w.r.t.x. using the formulae for differentiation of `"u"/"v" and 1/"v"` respectively
Select the correct answer from the given alternative:
Suppose f(x) is the derivative of g(x) and g(x) is the derivative of h(x).
If h(x) = a sin x + b cos x + c then f(x) + h(x) =
