![]() The differentiation of a constant is 0 as per the power rule of differentiation. What is The Differentiation of a Constant? To know more applications of differentiation, click here. We use the differentiation formulas to find the maximum or minimum values of a function, the velocity and acceleration of moving objects, and the tangent of a curve. What Are The Applications of Differentiation Formulas? Constant Rule: y = k f(x), k ≠ 0, then d/dx(k(f(x)) = k d/dx f(x). ![]() Chain Rule: Let y = f(u) be a function of u and if u=g(x) so that y = f(g(x), then d/dx(f(g(x))= f'(g(x))g'(x).Quotient Rule: If y = u(x) ÷ v(x), then dy/dx = (v.du/dx- u.dv/dx)/ v 2.Product Rule: If y = u(x) × v(x), then dy/dx = u.dv/dx v.du/dx.Sum Rule: If y = u(x) ± v(x), then dy/dx = du/dx ± dv/dx. Derivative Calculator with step-by-step Explanations     sin cos tan ( ) del u / v ÷ × sin -1 cos -1 tan -1 xn ex 7 8 9 csc sec cot ln log 10 4 5 6 sinh cosh tanh n 1 2 3 x sinh -1 cosh -1 tanh -1 0.The differentiation rules are power rule, chain rule, quotient rule, and the constant rule. There are different rules followed in differentiating a function. We know, slope of the secant line is \(\dfraccos(x Δx) = cos x\)] What Are The Differentiation Rules in Calculus? The slope of a curve at a point is the slope of the tangent line at that point. Take another point Q with coordinates (x h, f(x h)) on the curve. Let us take a point P with coordinates(x, f(x)) on a curve. The first principle of differentiation is to compute the derivative of the function using the limits. Use logarithmic differentiation to find the first derivative of f (x) (5 3x2)7 6x2 8x 12 f ( x) ( 5 3 x 2) 7 6 x 2 8 x 12. The geometrical meaning of the derivative of y = f(x) is the slope of the tangent to the curve y = f(x) at ( x, f(x)). ![]()
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