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neutron star
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Homework Statement
Find the derivative of the given function
z=(te^6t + e^7t)^5
Homework Equations
The Attempt at a Solution
5(te^6t + e^7t)^4
lurflurf said:write
z=(te^6t + e^7t)^5=(t+e^t)e^30t
The derivative of e^x is simply e^x itself. This can be derived using the limit definition of a derivative or by recognizing that e^x is its own derivative.
To find the derivative of e^u, use the chain rule. This involves taking the derivative of the outer function (e^x) and multiplying it by the derivative of the inner function (u). The result will be e^u times u'.
No, the derivative of e is always positive. This is because e is a constant value and its derivative is simply itself.
The derivative of ln(x) is simply 1/x. This can be derived using the properties of logarithms or by using the inverse function rule.
To find the derivative of e^x^2, use the chain rule twice. First, take the derivative of the outer function (e^u) where u = x^2. This will result in e^x^2 times 2x. Then, take the derivative of the inner function (x^2) which is 2x. Multiply these together to get the final result of 2xe^x^2.