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Galina-37 [17]
2 years ago
12

Y=sech(tan‐¹x) find the derivative ​

Mathematics
1 answer:
Klio2033 [76]2 years ago
8 0

Recall that

d/dx sech(x) = - sech(x) tanh(x)

d/dx tan⁻¹(x) = 1/(1 + x²)

Then by the chain rule,

dy/dx = - sech(x) tanh(x) / (1 + x²)

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Suppose xy=4 and dy/dt=-2. Find dx/dt when x=-3
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Dy/dx = dy/dt  *   dt/dx

xy = 4

y + x(dy/dx) = 0      by implicit differentiation. 

x(dy/dx) = -y

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<span>dy/dx = dy/dt  *   dt/dx             dy/dt = -2
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When x = -3,   xy = 4,  y = 4/x = 4/-3 = -4/3

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