I'm doing some mathematical calculation of some symbolic math that includes multiplication and differentiation of some matrices.
Some of the parameters in my calculations are functions of time...

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...

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...

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...
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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...
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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...
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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...
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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....
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