2. Find the derivative. Simplify if possible. y = x (arcsinh)(x/9) - sqrt(81 + x^2)? - sqrt{ } !,81
2. Find the derivative. Simplify, if possible. y = x (arcsinh) (x / 9) - sqrt (81 + x ^ 2)?
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It is a hyperbolic function
Monday, February 8, 2010
Sqrt{ } !,81 2. Find The Derivative. Simplify If Possible. Y = X (arcsinh)(x/9) - Sqrt(81 + X^2)?
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2 comments:
xarcsinh y = (x / y) - √ (81 + x ^ 2)
dy / dx = arcsinh (X / A) d / dx 1 + xd/dx1 / √ [(x ^ 2 / 9) 1) d / dx 1 / 9
.- 1 / 2 (81 + x ^ 2) ^ -1 / 2 d / dx 2x
arcsinh = (x / y) + x / √ (x ^ 2 +81)-x / √ (81 + x ^ 2)
= Arcsin (x / a) reaction / /
Ok
I will try to do step by step:
y '= [x (arcsinh) (x / 9)] - [sqrt (81 + x ^ 2)]
y '= (x)' (arcsinh) (x / 9) + x [(arcsinh) (x / 9)] - [sqrt (81 + x ^ 2)]
= Y '(arcsinh) (x / 9) + x / sqrt (1 + (x ^ 2 / 81)) - 2x / 2sqrt (81 + x ^ 2)
= Y '(arcsinh) (x / 9) + sqrt 3x / (81 + x ^ 2) - x / sqrt (81 + x ^ 2)
= Y '(arcsinh) (x / 9) + 2x / sqrt (81 + x ^ 2)
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