d/dx[eᵘ]
eᵘu’
To differentiate eᵘ with respect to x, we need to use the chain rule of differentiation.
Let y = eᵘ, where u is a function of x.
Applying chain rule, we get:
dy/dx = dy/du * du/dx
Now, differentiating eᵘ with respect to u, we get:
dy/du = eᵘ
Differentiating u with respect to x, we get:
du/dx
Therefore, putting these values in the chain rule formula, we get:
d/dx[eᵘ] = dy/dx = dy/du * du/dx = eᵘ * du/dx
Hence, the derivative of eᵘ with respect to x is eᵘ times the derivative of u with respect to x.
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