Derive the product rule for the differentiation of the product of three differentiable functions, that is , d/dx(f(x)g(x)h(x)). Thank You!
A curve has the equation y= (x-a)√(x-b) for x≥b, where a and b are constants. It intersects the x-axis at the point A with x=b+1. Show that the gradient of the curve of A is 1. Thank...
Given that y= x√(3-x2) , show that dy/dx = (3+2x2) / (√3+x2 ) . Is it possible to get a positive x value? My answer is (3-2x2) / √(3-x2 ) . Thank...
Given that y= (x2+1)n, where n is a positive integer, show that the ratio of dy/dx when x =1 to d2y/dx2 =1:n. Thank you!
Given that y= 1/√(x2 +3), show that (x2 +3) dy/dx +xy =0 Thank You!
1. Find the slope of the function y=2cosxsin2x at x=π/2 2. Find the equation of the line that is tangent to y=x2sin(2x) at x=-π 3. Determine the second derivative for...
Differentiate the function. p(r) = r^6 - (2/(5√r)) +r -1 Show all your work.
Quotient Rule Explanation Similar to product rule, the quotient rule is a way of differentiating the quotient, or division of functions. The quotient rule is defined as the quantity of the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator all over the denominator squared. The Formula for the Quotient Rule The... read more
Product Rule Explanation It is not always necessary to compute derivatives directly from the definition. Several rules have been developed for finding the derivatives without having to use the definition directly. These rules simplify the process of differentiation. The Product Rule is a formula developed by Leibniz used to find the derivatives of products of functions. The Product... read more
Mean Value Theorem Explanation The Mean Value Theorem states that, given a curve on the interval [a,b], the derivative at some point f(c) where a < c="">< b="" must="" be="" the="" same="" as="" the=""> slope from f(a) to f(b). In the graph, the tangent line at c (derivative at... read more
List of Derivatives Simple Functions Proof Exponential and Logarithmic Functions Proof Proof Proof Trigonometric Functions Proof Proof Proof Proof Proof Proof Inverse Trigonometric Functions Proof Proof Proof Proof Proof Proof... read more
Differentiation - Taking the Derivative Differentiation is the algebraic method of finding the derivative for a function at any point. The derivative is a concept that is at the root of calculus. There are two ways of introducing this concept, the geometrical way (as the slope of a curve), and the physical way (as a rate of change). The slope of a curve translates to the rate of... read more
Chain Rule Help The chain rule is similar to the product rule and the quotient rule, but it deals with differentiating compositions of functions. If we recall, a composite function is a function that contains another function: The Formula for the Chain Rule The capital F means the same thing as lower case f, it just encompasses the composition of functions.... read more