Find the derivative of the following functions.
y = x si...

Question

Find the derivative of the following functions.

y = x sin x

Accepted Answer

Welcome back, everyone. Find the derivative of the function Y equals X2 cosine of X. We're given four answer choices A says Y equals -2 X cosine x plus X2 X. B says Y equals. 2 X cosine x minus X2 X. C says Y equals 2 X cosine x plus x x and D says Y equals 2 x cosine x minus X2 X. So we want to find the first derivative of the function y equals x2 cosine of x, and this function involves a product. We can define two functions. The first one is X2, and the second one is G equals cosine of x. Now if we have a product of these two functions F and G, we can write that Y equals F multiplied by G, right, and we want to evaluate this derivative, so this means that we have to apply the product rule. Let's recall that the product rule states that F multiplied by G derivative is F multiplied by G plus F multiplied by G. And essentially what we want to do is evaluate each derivative. So we're given F, we can evaluate F and F is the derivative of X2d. Based on the power rule, while we bring down the exponent, we get 2, and the original exponent decreases by 1 unit, so 2 minus 1, and this gives us 2 X. Now the derivative of G is the derivative of cosine of x. And based on the table of basic derivatives, we have negative sin of X. So we have all of the components that we need and then the Y becomes F which is 2 X. Multiplied by G which is cosine x. And then we are adding F multiplied by G, but G has a negative sign, so instead of adding, we're going to say we are subtracting F, which is X2d multiplied by sin x. We have already incorporated the negative sign, so we get minus X2 X. So we have got the first derivative, and we can say that based on our answer, the correct answer to this problem corresponds to the answer to the. Thank you for watching.

Find the derivative of the following functions.y = x sin x

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Find the derivative of the following functions.
y = x sin x