Find dx/dt given x = sqrt(1 + cot 3t)?

Answer 1

Remember d/dx (f(x))^n = n(f(x))^(n-1) * d/dx f(x)

remember that sqrt(x) = x^(1/2)

then

d/dt (1+cot(3t))^(1/2) = 1/2 (1+cot(3t)^(-1/2) d/dt (1+cot(3t))

d/dt (1+cot(3t)) = -3(csc(3t))^2

and the final answer is

-3/2 (1+cot(3t))^(-1/2) (csc(3t))^2


Doug

Answer 2

Differentiate outside the brackets, leaving what is inside the brackets alone. Then multiply the result by the differential of what is inside the brackets.

x = sqrt(1 + cot 3t)
x = (1 + cot 3t)^(1/2)

dx/dt = (1/2)[(1 + cot 3t)^(-1/2)](-3cosec^2 3t)

Answer 3

X = √(1+cot3t)

dx/dt = 1/2 ( 1+cos3t) -½ [0 - cosec² 3t(3)]

dx/dt = 1/2{ 1/(1+cost3t)½ } {-3cosec² 3t}

= [ (-3/2 ) (cosec²3t) {1/(1+cos3t)½} ]

Hope it helped!

Answer 4

You're just bored, aren'tcha?

Answer 5

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