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1irishman
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Homework Statement
differentiate the following funtion: g(x) = x^3*e^-1/x + 3^x*ln(1/x)
Homework Equations
chain rule and product rule
The Attempt at a Solution
x^3*d/dg(e^-1/x)d/dg(x)^3 + 3^x
sorry...i am very confused!
yes i think it is:╔(σ_σ)╝ said:In order to serve you better can you please state the chain rule.
╔(σ_σ)╝ said:Lets look at the function g(x) in parts. Let's consider the first part...
x^3(e^(-1/x))
You need the chain rule and the product rule to differentiate this term. Can you try differentiating it again ?
that was my attempt at differntiating the first part.╔(σ_σ)╝ said:I have no idea of what you just said...
╔(σ_σ)╝ said:How?
Okay what is the derievative of x^3 and of e^(1/x) ?
Isn't f(x)=e^-1/x?Dick said:There's nothing wrong with ╔(σ_σ)╝'s advice. Maybe a little abrupt with not going into the chain rule a little more but you are missing it. You've already stated the chain rule f'(g(x))g'(x). In the case of e^(-1/x) that makes f(x)=e^x and g(x)=(-1/x), right? What's the derivative of f and the derivative of g and can you put them into that chain rule formula?
actually nevermind1irishman said:Isn't f(x)=e^-1/x?
No. Please carefully read dick's post again. Besides, I already gave the answer 2 post ago.1irishman said:-e^x/x^3 ?
Differentiation is a mathematical process used to find the rate of change of a function at a specific point. It involves finding the slope of the tangent line to the curve at that point.
The steps to differentiate a function are as follows:
Differentiation is used in many fields, including physics, engineering, economics, and biology. It is used to calculate rates of change, such as velocity, acceleration, and growth rates. It is also used in optimization problems to find the maximum or minimum value of a function.
No, not all functions can be differentiated. A function must be continuous and have a defined rate of change at every point in order to be differentiated.
Differentiation and integration are inverse operations. Differentiation is used to find the rate of change of a function, while integration is used to find the area under a curve. In other words, differentiation is a process of finding the derivative of a function, while integration is a process of finding the anti-derivative of a function.