1. Write the precise definition for a function f(x) defined for all values of x to be a differentiable function. 2. Can someone explain to me how the dervative of sin(x^2) is 2x cos (x^2)?
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Originally Posted by Nimmy 2. Can someone explain to me how the dervative of sin(x^2) is 2x cos (x^2)? Use the chain rule. Let $\displaystyle f(x) = sin(x)$ and $\displaystyle g(x) = x^2$ So $\displaystyle \frac{d}{dx}(f(g(x)) = f'(g(x)) \cdot g'(x)$ $\displaystyle \frac{d}{dx}(sin(x^2)) = cos(x^2) \cdot 2x$ -Dan
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