d/dx (u^n)
To differentiate the function u raised to the power of n with respect to x, we can use the chain rule
To differentiate the function u raised to the power of n with respect to x, we can use the chain rule. The chain rule states that if we have a composite function, f(g(x)), then the derivative of that function with respect to x is given by:
d/dx (f(g(x))) = f'(g(x)) * g'(x)
In our case, u is the base and n is the exponent, and we want to find the derivative with respect to x. Applying the chain rule, we have:
d/dx (u^n) = d/du (u^n) * du/dx
The first term on the right-hand side involves differentiating u^n with respect to u, and treating n as a constant. The power rule states that the derivative of u^n with respect to u is given by:
d/du (u^n) = n * u^(n-1)
Applying this to our equation, we have:
d/dx (u^n) = n * u^(n-1) * du/dx
So, the derivative of u^n with respect to x is equal to n times u^(n-1) times the derivative of u with respect to x.
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