Deifferentiate: y=e^-3x+2
would the answer be -3e^-3x+2 or
3e^-3x+2
The "+2" is a constant, so when differentiated, it disappears.
d(e^(ax))/dx
=ae^(ax)
So if a=-3,
d(e^(-3x))/dx
=-3e^(-3x)
Be careful about parentheses please Hannah
thank you
Like perhaps you might have meant
y=e^(-3x+2)
dy/dx = -3 e^(-3x+2)
To differentiate the function y = e^(-3x+2), you can use the chain rule of differentiation.
The chain rule states that if you have a composition of functions, such as f(g(x)), the derivative of this composition can be found by multiplying the derivative of the outer function (f'(g(x))) with the derivative of the inner function (g'(x)).
In this case, the outer function is e^x and the inner function is -3x+2.
The derivative of the outer function e^x with respect to x is simply e^x, and the derivative of the inner function -3x+2 with respect to x is -3.
Now, applying the chain rule, we can find the derivative of y = e^(-3x+2):
dy/dx = e^(-3x+2) * (-3)
Simplifying this expression gives:
dy/dx = -3e^(-3x+2)
So, the correct answer is -3e^(-3x+2).