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2.2: Definition of the Derivative - Mathematics LibreTexts
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WebProduct Rule - Part 1 Let \( f(x)=-5 x^{4} \) and \( g(x)=-7 x^{5} \) so that \( h(x)=f(x) \cdot g(x) \). Their; Question: Follow the steps to find the derivative of the given function in … WebFind the derivative with respect to x. (1/y) (dy/dx) = x (1/x) + lnx (1) (to find the derivative of xlnx, product rule is used) (1/y) (dy/dx) = 1 + lnx Multiply both sides by y. dy/dx = y (1 + lnx) Substitute y = x x. dy/dx = x x (1 + lnx) Therefore, the derivative x x is xx(1 + lnx). Example 2 : Find the derivative of a x with respect to x. or WebFind the Derivative - d/dx f (x)=7/ ( square root of x) f (x) = 7 √x f ( x) = 7 x Use n√ax = ax n a x n = a x n to rewrite √x x as x1 2 x 1 2. d dx [ 7 x1 2] d d x [ 7 x 1 2] Since 7 7 is constant with respect to x x, the derivative of 7 x1 2 7 x 1 2 with respect to x x is 7 d dx [ 1 x1 2] 7 d d x [ 1 x 1 2]. 7 d dx [ 1 x1 2] 7 d d x [ 1 x 1 2] great martial arts fights