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Answer :
Final answer:
The problem involves differentiation and finding the equation of a tangent line to a curve. The derivative of the function can be found using the chain and power rules of differentiation, after which we can substitute to find f'(1). Additionally, the equation of a tangent can be found using the point-slope form of the line equation.
Explanation:
This problem involves differentiation from first principles, i.e. using the basic definition of a derivative. The given equation is
f(x)+xâµ(f(x))²=34
. If we are given that
f(1) = 2
, we can find
f'(1)
by taking the derivative of our function f(x) with respect to x using the chain rule together with the power rule. Subsequently, finding f'(1) becomes a substitution problem. The other part of the question may involve finding the equation of a tangent line to a curve at a specific point, x=5, with a negative slope using the equation
y = mx+b
, where m is the slope of the line and b is the y-intercept. Unfortunately, the provided reference information does not seem to be directly useful for this problem.
Learn more about Derivatives and Tangent Lines here:
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