Find the derivatives of the functions r=sin⁡2θ

Question

Alannej · Accepted Answer

Step 1
According to the question, we have to find the derivative of the expression,

r = \sin \sqrt{2} θ

.
The derivative of a function y=f(x) of a variable x is a measure of the rate at which the value y of the function changes with respect to the change of the variable x.
Here the function is r and variable is

θ

, to differentiate the function, we have to use the formula as given below,

\frac{d}{d θ} (\sin θ) = \cos θ

.
Step 2
Rewrite the given expression,

r = \sin \sqrt{2} θ

Now, differentiate the above function with respect to

θ

and solving further,

r = \sin \sqrt{2} t h e t

\frac{d r}{d θ} = \cos \sqrt{2} θ \cdot \frac{d}{d θ} (\sqrt{2} θ)

= \cos \sqrt{2} θ \cdot \sqrt{2}

= \sqrt{2} \cos \sqrt{2} θ

So, the derivative is

\sqrt{2} \cos \sqrt{2} θ

.
Hence, the derivative of the function

r = \sin \sqrt{2} θ i s \sqrt{2} \cos \sqrt{2} θ

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

Find the derivatives of the functions r=\sin\sqrt{2}\theta

Answered question

Answer & Explanation

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