![]() ![]() What Is the Difference Between Chain Rule Formula and Product Rule? To find the time rate of change of the pressure, to calculate the rate of change of distance between two moving objects, to find the rate of change of the average molecular speed, we apply the chain rule. This chain rule has broad applications in physics, chemistry, and engineering. The chain rule formula is mainly used to find the derivative of a composite function (a function that is the combination of two or more functions). What Are the Applications of Chain Rule Formula? When x here is replaced with something else here, say, d/dx(sin 3x) =? In such cases, we apply the chain rule formula which says d/dx ( f(g(x) ) = f' (g(x)) Usually, all the derivative formulas are in terms of x, for example, d/dx (sin x) = cos x. There are two forms of the chain rule formula. The chain rule formula is used to find the derivative of a composite function (i.e, when one function is inside the other). If there exists a function f of g which in turn is a function of u(x), then the instantaneous change in f with respect to x is given as change in f/ change in x = change in g /change in u × change in u /change in x. The chain rule is used to find the derivative of a composite function. Thus the equation of the tangent line to the given function y = (5 x 4 - 2) 3 applying the chain rule formula is y = 540x - 513 Hence substitute (1,27) in the equation of the tangent line, y = 540x + b, we get We need to find the equation of the tangent line. Therefore the equation of the tangent line in the slope-intercept form is y = mx+ b ⇒ 27 = 540x + b We need to evaluate the function and the derivative at the given point We know that the derivative of the function gives the slope of the line at the given point. ![]() Let us apply the chain rule to find the equation of the tangent line to the given function y = (5 x 4 - 2) 3 at x = 1.
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