How do you find the derivative of y equals 7e-6x?

Answer 1

13

Answer 2

I can see two likely intentions of this question. You wish to find the derivative of either:

y=7e-6x

or

y=7e-6x

For the first option, we use the fact that 7e is a constant (e is a number, not a variable, and a number times a number is still a number) to know that the derivative of the subcomponent 7e is zero. For the subcomponent -6x, we can use the power rule. Its derivative is (-6)(1)x1-1=-6x0=(-6)(1)=-6. So, in the end, we get:

y'=-6

For the second option, we use the chain rule. For a function that contains another function in itself, you must first derive the outer function and then multiply that by the derivative of the inner function. For this function, the "outer" function is ex, while the "inner" function is -6x. The derivative of ex is ex, and the derivative of -6x is -6. In the end, we get:

y'=(outer function derivative)(inner function derivative)=(7e-6x)(-6)=-42e-6x

y'=-42e-6x