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Find the equation of the tangent to the curve y = (5x+4)/(3x -8) at the point (2, -7)

(Much easier to explain in conversation and with drawings): But, An application of the quotient rule, stating that for f(x)=a(x)/b(x), f'(x) = a'(x)b(x) - a(x)b'(x) all over [b(x))]^2 Here, a(x) = 5x + 4 and...
BR
Answered by Ben R. • Maths tutor
6075 Views

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...
PD
Answered by Pria D. • Maths tutor
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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
7438 Views

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
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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
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