user: I'm in the process of buying a new home and have been working out the financials. I've just secured a loan for $350,000 with a 3.5% interest rate, and the loan period is set for 30 years. Could you help me figure out what my monthly mortgage payment would be?

On a different note, my niece asked me for some help with her math homework, and I thought you might assist. She's learning about least common multiples and was tasked to find the LCM of 15 and 25. Could you provide that as well?

Also, she's working on factorials and got stuck on calculating 7!. It would be great if you could show us the result of that.

Lastly, I've been brushing up on my calculus and was trying to estimate the derivative of the function f(x) = 3x^2 + 2x - 1 at the point where x equals 5. I’d appreciate it if you could help me with this calculation too.

Available functions:
name: mortgage_calculator
description: Calculates the monthly mortgage payment.
parameters: type: dict
properties: loan_amount: type: float
description: The amount of the loan.
interest_rate: type: float
description: The interest rate of the loan, ranging from 0 to 1.
loan_period: type: integer
description: The period of the loan, in years.
required: loan_amount
interest_rate
loan_period
name: math_lcm
description: Calculates the least common multiple of two numbers.
parameters: type: dict
properties: a: type: integer
description: The first number. This should be the larger number.
b: type: integer
description: The second number.
required: a
b
name: math_factorial
description: Calculates the factorial of a number.
parameters: type: dict
properties: n: type: integer
description: The number to calculate the factorial of.
required: n
name: estimate_derivative
description: Estimate the derivative of a function at a given point.
parameters: type: dict
properties: function: type: string
description: The function to calculate the derivative of.
x: type: integer
description: The point to calculate the derivative at.
required: function
x