dy/dx e^x
The derivative of the exponential function e^x with respect to x, denoted as dy/dx e^x, can be found using the chain rule of differentiation
The derivative of the exponential function e^x with respect to x, denoted as dy/dx e^x, can be found using the chain rule of differentiation.
The chain rule states that if we have a composite function, such as y = f(g(x)), where f and g are differentiable functions, then the derivative of the composite function can be calculated as the derivative of the outer function f evaluated at the inner function g(x), multiplied by the derivative of the inner function g(x) with respect to x.
In this case, our composite function is y = e^x, where f(u) = e^u and g(x) = x.
Let’s calculate dy/dx e^x step by step:
1. Find the derivative of the outer function f(u) = e^u:
df/du = d(e^u)/du = e^u
2. Find the derivative of the inner function g(x) = x:
dg/dx = d(x)/dx = 1
3. Apply the chain rule to find dy/dx e^x:
dy/dx = (df/du) * (dg/dx) = e^u * 1 = e^x
Therefore, the derivative of e^x with respect to x, dy/dx e^x, is equal to e^x.
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