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jpc90
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How do you differentiate f(x)=arctan(e^5x)
The derivative of f(x) = arctan(e^5x) is given by f'(x) = (e^5x)/(1 + e^(10x)). This can be derived using the chain rule and the derivative of arctan function.
To find the critical points of f(x) = arctan(e^5x), we need to find the values of x where f'(x) = 0. This will give us the stationary points of the function, which can be considered as critical points.
Yes, f(x) = arctan(e^5x) is a continuous function. Both the arctan function and the exponential function are continuous, and the composition of continuous functions is also continuous.
The range of f(x) = arctan(e^5x) is (-π/2, π/2). This is because the range of the arctan function is (-π/2, π/2), and the range of e^5x is (0, ∞). The composition of these two functions will give us the intersection of their ranges.
To sketch the graph of f(x) = arctan(e^5x), we can use the properties of the arctan function and the exponential function. We can also plot a few points and use them to draw a smooth curve. The graph will have a horizontal asymptote at y = π/2 and a vertical asymptote at x = 0.