Find the derivative of the function f by using the rules of...

Transcript

00:01 In the given question, we are told to find the derivative of the function f of x, which is given as minus x cube plus 8x square minus 3.

00:14 And we are told to solve this using the derivative and find the derivative using rules of differentiation.

00:21 So the first rule that we can use is when we are differentiating the sum of let's say one or two functions, not one, more than one functions, what we could do is we can differentiate each one of them and add their results to get the differential of the entire function, right? so over here if our function has three parts, p, q and r, we can differentiate them as the differential of p plus differential of q plus differential of r.

00:57 So using this rule, we are going to differentiate over here and while differentiating this particular function we can use a general property which is that when we differentiate when we differentiate functions of the form x to the power of n the result would be n times x to the power of n minus 1 so this is one rule that we can use and the other one is when we differentiate a constant when we differentiate a constant the result is equal to zero so keeping these in mind what we can do now is we can write f dash x would be equal to first what we could do is we could take minus one times x to the power three would be three times x to the power of three minus one plus eight x squared would be eight times we are differentiating x squared so it would be two times x to the power of 2 minus 1 and lastly we have a function so on differentiating 3 with respect to x we will have the result as 0 this is what we would have as f of x f dash x so now on simplifying minus 3 times x to the power of 3 minus 1 is 3 x squared so minus 1 times 3x squared is minus 3x squared.

02:39 Then 2 times x to the power of 2 minus 1 is 1...

Question

Find the derivative of the function $f$ by using the rules of differentiation.\\ $f(x) = 2x^3 - 9x^2 + 3$\ $f'(x) = $

Question

Find the derivative of the function $f$ by using the rules of differentiation.\\ $f(x) = 2x^3 - 9x^2 + 3$\ $f'(x) = $

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