To differentiate Y with respect to x, we can use the power rule and the chain rule of differentiation.
Y = x + 1/√x
Y' = d/dx(x) + d/dx(1/√x)
Applying the power rule and chain rule:
Y' = 1 + (-1/2)x^(-3/2)
Simplifying the second term:
Y' = 1 - 1/(2x^(3/2))
Therefore, the derivative of Y with respect to x is:
Y' = 1 - 1/(2x^(3/2))
To differentiate Y with respect to x, we can use the power rule and the chain rule of differentiation.
Y = x⁴ + √x
Y' = d/dx(x⁴) + d/dx(√x)
Applying the power rule and chain rule:
Y' = 4x³ + (1/2)x^(-1/2)
Simplifying the second term:
Y' = 4x³ + 1/(2√x)
Therefore, the derivative of Y with respect to x is:
Y' = 4x³ + 1/(2√x)
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Can you get the 2nd and 3rd order differential of this: Y= x+1/√x
Sure, we can find the 2nd and 3rd order derivatives of Y with respect to x using the power rule and the chain rule of differentiation.
First, let's find the first derivative of Y:
Y = x + 1/√x
Y' = 1 - 1/(2x^(3/2))
Next, we can differentiate Y' to find the second derivative:
Y'' = d/dx(1 - 1/(2x^(3/2)))
Using the power rule and chain rule:
Y'' = 3/(4x^(5/2))
Therefore, the second derivative of Y with respect to x is:
Y'' = 3/(4x^(5/2))
To find the third derivative of Y, we differentiate Y'' with respect to x:
Y''' = d/dx(3/(4x^(5/2)))
Using the power rule and chain rule:
Y''' = -15/(8x^(7/2))
Therefore, the third derivative of Y with respect to x is:
Y''' = -15/(8x^(7/2))