F(x)+x4[f(x)]3=2005f(x)+x4[f(x)]3=2 005 and f(2)=5f(2)=5, find f′(2)


we went over this in class but she only showed us how to get it to dy/dx and not how to actually get a number i really need on this!
calculus is horrible

Differentiating both sides yields



The right hand side is a constant, so the derivative is just 0, and . The remaining term requires using the product rule:



Using the power rule for the first term here and the power/chain rules for the second gives




Putting everything together, you have



Collecting the terms with gives





Now, finding the value of the derivative at is just a matter of plugging in :



We know , so we get