A differential equation is an equation involving a function and one or more of its derivatives. Determine whether the function y=πsinθ+2πcosθ is a solution to the differential equation d^2y/dθ^2...
A piece of plexiglass is in the shape of a semicircle with radius 2 m. Determine the dimensions of the rectangle with the greatest area that can be cut from the piece of plexiglass.
Air is being pumped into a spherical balloon. The volume, V, in cubic centimetres, of the balloon is V=4/3πr^3, where the radius, r, is in centimetres. a) Determine the...
Show that there is no polynomial function that has a derivative of x^-1.
Determine equations for the tangents to the cubic function y=2x^3 -3x^2 -11x +8 at the point where y=2.
Determine equations for two lines that pass through the point (1,-5) and are tangent to the graph of y=x^2-2.
A video describing the steps of logarithmic differentiation with an example.
Review how to take the derivative of logarithmic functions. The sample problem is taken from IB Math SL, Section 23C. Recorded November 2013.
f'(x) = 2(2/3)x-1/3 - (5/3)x2/3 = (4/3)x-1/3 - (5/3)x2/3 f"(x) = (4/3)(-1/3)x-4/3 - (5/3)(2/3)x-1/3 = (-4/9)x-4
how would I set the 1st and 2nd derivatives to zero and solve for x ?
find 1st and 2nd derivative for x to the 2/3 * (2-x) = x to the 2/3 * (2-x) sorry I didn't clarify
find the 1st and 2nd derivative
please answer, i dont understand how to go about this problem.
Urgent! Please help me! I have an exam in two days and I really need help with these questions. Please explain the steps and answers as thoroughly as possible.
1. Find the derivative f'(x). (a) f(x)=xexcosx (b) f(x)=secxtanx (c) f(x)=sinx/1+cosx 2. Let g(x) be a differentiable function such that g(0)=2 and g'(0)=3. (a)...
f(x)= (5x2 -7)(x2-2) / x2+6 find f ' (x) at x=5
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
Derivative Proofs Though there are many different ways to prove the rules for finding a derivative, the most common way to set up a proof of these rules is to go back to the limit definition. This way, we can see how the limit definition works for various functions. We must remember that mathematics is a succession. It builds on itself, so many proofs rely on results... read more