Find the derivative of the function x^2cos x.
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EXPLANATION.
Derivative of the function x²cosx.
As we know that,
By using the the product rule.
⇒ d[f(x).g(x)]/dx = f(x).d[g(x)]/dx + g(x).d[f(x)]/dx.
By applying this formula in equation, we get.
⇒ d[x²cosx]/dx = x²d[cos x]/dx + cos x d[x²/dx.
⇒ d[x²cosx]/dx = x²(-sin x) + cos x(2x).
⇒ d[x²cosx]/dx = 2xcos(x) - x²sinx.
MORE INFORMATION.
Differentiation of f(x), g(x) type function.
When base and power both are the functions of x that is the function is of the form [f(x)]^g(x).
⇒ y = [f(x)]^g(x).
⇒ ㏒(y) = g(x) ㏒[f(x)].
⇒ 1/y.dy/dx = d g(x).㏒[f(x)]/dx.
⇒ dy/dx = [f(x)]^g(x) . [d[g(x)㏒f(x)]/dx
⇒ That is dy/dx = Q.d/dx (power x ㏒ base).
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