The product rule is a common rule for the differentiating problems where one function is multiplied by another function. Learn how to apply this product rule in differentiation along with the example at BYJU’S.
The product rule is solved by dividing each part of the product into functions then plugging the functions in the product rule equation. Then solve the derivatives, and multiply and add the terms. What is the product rule equation? The product rule equation is (f(x)*g(x))' = f(x)' ...
6. Rules for computing derivatives (product rule, quotient rule and chain rule); formulas for all relevant functions, including implicitly defined functions (derive y with respect to x=dy/dx) Unit IV. Applications of Derivatives 1. Finding extrema: f’(x)=0, decide if it is a extrema usin...
Product Rule| ( f (x) )( g (x) ) Quadratic Formula Quotient Rule| ( f (x ) ) / ( g (x) ) Relative Extrema sin(a*x) Derivative sin(a*x) Integral sin(a*x) Integral sin(x)^3*cos(x)^2 tan(a*x) Derivative Trig & Half Angle Formulas & Identities| sin(u)*cos(v) | ...
2.“Calculus: Early Transcendentals” by Stephen Davis, Howard Anton, and Irl Bivens: This is another excellent comprehensive text. The “Early Transcendentals” part means that the book introduces the concept of the transcendental functions(超越函数) (such as exponential(指数的) and logarithmic(对...
3Differentiation Rules Derivatives of Polynomials and Exponential Functions The Product and Quotient Rules Derivatives of Trigonometric Functions The Chain Rule,Implicit Differentiation Derivatives of Logarithmic Functions Exponential Growth and Decay Related Rates ...
Problem 3. Calculate the derivative of 5x sin x.5x cos x + 5 sin xThe power rule6. d dx xn = nxn−1"The derivative of a power of xis equal to the product of the exponent timesx with the exponent reduced by 1."That is called the power rule. For example,...
Thedot productrepresents the similarity between vectors as a single number: For example, we can say that North and East are 0% similar since(0,1)⋅(1,0)=0. Or that North and Northeast are 70% similar (cos(45)=.707, remember thattrig functions are percentages.) The similarity sho...
Using Trig Identities to Prepare Functions for Integration . . . . . . . . . . . . . . . . . . . . 96 Integrating Compositions of Functions with Linear Inputs . . . . . . . . . . . . . . . . . . . . 98 Answers and Explanations . . . . . . . . . . ....
Product Rule:The limit of the product of two functions is equal to the product of their limits. If LimX→c(f(X)) = L and LimX→c(g(X)) = M, then LimX→c[f(x)g(x)] = LM. Quotient Rule:The limit of the quotient of two functions is equal to the quotient of their limits...