![]() ![]() Here we are using the product rule and the derivative of sine x square will be equal to cos x, squared times the derivative of x square, which is nothing but 2 x. The derivative of x, divided by x square, now understand that the derivative of x, sine x square, that is right here, will be nothing but x, cos x, squared times 2 x, plus sine x, squared times 1. The whole dash the derivative of what is in the numerator minus x, sine x square minus sine x, squared times 1. We are going to use the quotient rule, so we will have x times x, sine x, square, minus sine x square. So the derivative of this function will be nothing but f dash of x. ![]() We will use all these 3 rules understand that this expression can be written as x times sine x square minus sine x, squared divided by x. Now, let's consider f of x, is equal to x, minus 1 times sine x, squared divided by x to compute the derivative of this expression. F, dash of x minus f of x times g dash of x, divided by g of x, the whole square. The derivative of this expression will be nothing but g of x times. A differentiation understand that chain rule is nothing, but the derivative of f of g of x is equal to f dash of g of x times g dash of x and in product rule derivative of f dot g can be computed as f dot g dash plus F dash times g and in quotient rule whenever we are having a function which is of f divided by g. In part, a we act as to make a function that requires chain rule product rule and quotient rule to compute. ![]()
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