What Is The Derivative Of Sin The previous answer contains mistakes Here is the correct derivation First of all the minus sign in front of a function f x sin x when taking a derivative would change the sign of a derivative of a function f x sin x to an opposite This is an easy theorem in the theory of limits limit of a constant multiplied by a variable equals to this constant multiplied by a limit of
1 sqrt 1 x 2 Let y sin 1x so siny x and pi 2 Answer 2sin x cos x Explanation You would use the chain rule to solve this To do that you ll have to determine what the outer function is and what the inner function composed in the outer function is In this case sin x is the inner function that is composed as part of the sin 2 x To look at it another way let s denote u sin x so that u 2 sin 2 x Do you notice
What Is The Derivative Of Sin
What Is The Derivative Of Sin
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Derivative Of Sin x From First Principles YouTube
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See all questions in Intuitive Approach to the derivative of y sin x Impact of this question 43918 views Calculus Differentiating Trigonometric Functions Differentiating sin x from First Principles 1 Answer Alan N
See below It is tedious and space consuming to use lim hrarr0 on every line so I hope you ll excuse my approach We ll simplify the difference quotient first then find the limit sin x h 2 sinx 2 h sinxcos h cos x sin h 2 sinx 2 h color red sin 2xcos 2h 2sinxcos h cosx sin h color blue cos 2xsin 2h In order to differentiate sin 3 x we need to use a chain rule which tells us that d dx f g x f g x g x Letting y sin 3 x then dy dx 3sin 2 x cos x In this problem we ve also performed the power rule namely by subtracting 1 from the power of 3 on the sin x term which is why we end up with a sin 2 x
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We have y xsin x Which is the product of two functions and so we apply the Product Rule for Differentiation Note that this matches the other answer as using the triangle we can also see that cos arctan x 1 sqrt x 2 1
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The previous answer contains mistakes Here is the correct derivation First of all the minus sign in front of a function f x sin x when taking a derivative would change the sign of a derivative of a function f x sin x to an opposite This is an easy theorem in the theory of limits limit of a constant multiplied by a variable equals to this constant multiplied by a limit of
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