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newatcalculus
What is the derivative of 5x^2 + 10x + 5? I'm new at calculus
here you can apply the power rule
When you are deriving polynomials, the important thing to remember is that you can derive each piece independently.
\[ 3x^3 + 5x + 10\] To find the first derivative you can apply the Power Rule For Example, in general, finding the derivative of a function with exponents follows such a pattern: \[x^{n} = n*x^{n-1}\] Turn the exponent into a coefficient and then subtract 1 from the exponent for the first derivative
Differentiate each terms
so you use that with misterf's idea, and work through each part of the function individually
very nice, antimatter. you can do that to each x term and then add them back together
What is a derivative? What does it represent?
it is the rate of change of function at a given value.
Derivative is like a function
which gives us the rate of change
In the physical world, for example, if you have a graph that shows the position of something, the derivative of that graph at a given point is the speed of the object at that point.
say your function represents your distance over time. if you take the derivative of that function, you will get a function for your speed.
of the function with respect to any independent variable
Likewise, if you have a graph (or function) describing the speed, the derivative at a given point gives you the acceleration at that point, i.e., the rate at which your speed is changing. Your speed is the rate at which your position is changing. Etc.
by the way derive is different from differentiate
derive means sort of like to find differentiate means to take the derivative
i think its very easy and simple method to find derivate