Differentiate and do not simplify.

y= e^(- sq.rt x) + e^3 - 2^(3x-1)

I have now answered 4 Calculus questions for "anonymous"

How about showing me what you know about this question.

To differentiate the given function, y = e^(-√x) + e^3 - 2^(3x-1), you can follow these steps:

Step 1: Differentiate each term of the function separately using the chain rule and power rule.

Term 1: y₁ = e^(-√x)
To differentiate this term, apply the chain rule by considering the derivative of the outer function (e^x) and the derivative of the inner function (-√x).

dy₁/dx = d/dx (e^(-√x))
= e^(-√x) * d/dx(-√x)
= e^(-√x) * -1/2 * (1/√x)
= -1/2√x * e^(-√x)

Term 2: y₂ = e^3
The derivative of any constant is always zero.

dy₂/dx = d/dx (e^3)
= 0

Term 3: y₃ = 2^(3x-1)
To differentiate this term, we use the power rule. Take note that the base is 2 and the exponent is a function of x.

dy₃/dx = d/dx (2^(3x-1))
= ln(2) * 2^(3x-1) * d/dx (3x-1)
= ln(2) * 2^(3x-1) * 3
= 3ln(2) * 2^(3x-1)

Step 2: Combine the derivatives of each term to get the final result.

dy/dx = dy₁/dx + dy₂/dx + dy₃/dx
= -1/2√x * e^(-√x) + 0 + 3ln(2) * 2^(3x-1)

Therefore, the derivative of y = e^(-√x) + e^3 - 2^(3x-1) is dy/dx = -1/2√x * e^(-√x) + 3ln(2) * 2^(3x-1).