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Math Tutor

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Unlock the power of math with this GPT prompt! Have ChatGPT/GPT3 act as your virtual math teacher. The prompt will provide clear and concise explanations of even the toughest mathematical equations and concepts. From step-by-step problem-solving to visual demonstrations, this prompt has you covered. Say goodbye to confusing textbooks and hello to a brighter understanding of math. Get started now and ace your next exam!
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1 year ago

Prompt Details

Chat - GPT-3.5 (gpt-3.5-turbo)
Token size
71 ($0.00010 / call)
Example input
explain the chain rule in calculus with examples
Example output
The chain rule is a fundamental concept in calculus that allows us to differentiate composite functions. In other words, it allows us to find the derivative of a function that is composed of two or more functions. The chain rule states that if we have a composite function f(g(x)), where g(x) is a differentiable function and f(x) is a differentiable function, then the derivative of f(g(x)) with respect to x is given by: f'(g(x)) * g'(x) This can be understood as finding the derivative of the outer function f(x) and multiplying it by the derivative of the inner function g(x). Here's an example to help illustrate this concept: Let f(x) = x^2 and g(x) = 2x. We want to find the derivative of the composite function h(x) = f(g(x)) = f(2x) = (2x)^2. Using the chain rule, we have: h'(x) = f'(g(x)) * g'(x) = 2 * (2x) * (2) = 8x So the derivative of h(x) = 8x. Another example: let f(x) = e^x and g(x) = sin(x). We want to find the derivative of h(x) = f(g(x)) = f(sin(x)) = e^(sin(x)). Using the chain rule, we have: h'(x) = f'(g(x)) * g'(x) = e^(sin(x)) * cos(x) So the derivative of h(x) = e^(sin(x)) * cos(x). I hope this helps! Let me know if you have any questions or would like to see additional examples.
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