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If y=cos(3x)cosec(4x), find dy/dx.

Use the product rule: Let u = cos3x , v = cosec4x Then du/dx = -3sin3x , dv/dx = -4cosec4xcot4x (standard result, given in the formula booklet) Hence dy/dx = -4cosec4xcot4xcos3x - 3sin3xcosec4x . (No simplif...
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Answered by Pria D. • Maths tutor
5181 Views

Find the coordinates of the turning point of y=e^(2x)*cos(x)?

Think about which process we need to determine the turning point? - Differentiation Think about the form of the given function. - Product of two functions, so use Product Rule for Differentiation -Process th...
AH
Answered by Abbas H. • Maths tutor
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Why is there always constant of integration when you evaluate an indefinite integral?

When you are asked to integrate a function f(x), you are really being asked the question: "what function F(x) exists such that when you take its derivative, you are left with f(x)?" Let us first co...
AS
Answered by Akhil S. • Maths tutor
4600 Views

Prove, using the product rule that, the derivative of x^{n} is nx^{n-1} where n is a natural number. What if n is an integer or n is rational?

We know that d / dx (x) = 1. Looking at x^2 as a specific example, and using the product rule, we see that d/dx(x^2) = xd/dx(x) + d/dx(x)x = x + x = 2x. Similarly for x^3, d/dx(x^3) = 3 * x^2 * d/dx(x) = 3 x...
AH
Answered by Alfred H. • Maths tutor
12930 Views

The line AB has equation 5x+3y+3=0. The line AB is parallel to the line with equation y=mx+7 . Find the value of m.

Rearrange first equation to show y=-5/3x-1 lines are parallel therefore gradient is the same m=-5/3
IC
Answered by Isabel C. • Maths tutor
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