Implicit differentiation: Logarithms

Given equation ln(y/x)=x^2y^2 Find dy/dx

Simplifying polynomial expressions.

How do I simplify: [(8x)/(3x-6)]x[(x2-4)/(2x+4)]

integrals - trigonometric subsitution

The integral is to be solved using trigonometric subsitution. I have attached a word document with the integral to solve and my work. I want to know if my answer is correct. If my answer is not correct, I want to know the correct answer and the steps to get it. Thanks.

trigonometric integrals involving powers

I used the product to sum identities rule since the integral involved cosines of different angles. I have attached a word document with the integral to solve and my work. I want to know if my answer is correct. If my answer is not correct, I want to know the correct answer and the steps to get it. Thanks.

Integral solved with partial fractions

Please see the attached file for the fully formatted problems. The integral is to be solved using partial fractions.

Sum of a series

I am stuck on how to solve the sum of the series that I have attached in a word document.

Calculating integrals: Sines and Cosines

Integrate {cos(x)cos(3x)cos(5x),x}

Simple Vector Cross Product Proof

Create a proof to show that the following is true. a x (b+c) = a x b + a x c

Finding the equation of the straight line which is tangent to the curve

For the curve f(x) = x - 1/3x^2 (one third x squared), find the equation of the straight line which is tangent to this curve at the point x = 1. See attachment for diagram. I have made a tabulation of values for x = -2 to +5 and found that the point on the tangent touching the curve is (1, 0.6(recurring)) - I think this i ...continues

Derivatives: Chain Rule

Please see the attached file for the fully formatted problems. For a composite function f(x) = g(u(x)) state the chain rule for the derivative f(x). For each of the following functions, compute the derivative, simplifying your answers. f(x)=ln(1 + x^2) f(x)= sin(x^2) f(x) = (sin x)^2