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dy/dx = 10exp(2x) - 4; when x = 0, y = 6. Find the value of y when x = 2.

First, we must evaluate what is given in the question. As it can be seen, the expression indicates that the problem consists of a first-order differential equation. We are also given the values of x and thei...
GL
Answered by Girts L. • Maths tutor
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what is the geometrical meaning of the derivative of a function f?

The derivative of a function f(x), usually denoted as f'(x), gives you the gradient of the graph of f(x) for every point x in the domain of f. Therefoore, the derivative of a funtion can show how fast/slow a...
TG
Answered by Theodore G. • Maths tutor
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Differentiate implicitly with respect to x the equation x^3*y^5+3x=8y^3+1

3x 2 y 5 +5x 3 y 4 y'+3 = 24y 2 y' 3x 2 y 5 +3 = (24y 2 –5x 3 y 4 )y' y' = (3x 2 y 5 +3) / (24y 2 –5x 3 y 4 )
NG
Answered by Nora G. • Maths tutor
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Having x(x+4)=y, calculate dy/dx

Considering that x(x+4) = x^2+4x, and having that the derivative of the sum is the sum of the derivatives. dx/dy x^2 = 2x and dx/dy 4x = 4 , then dx/dy x(x+4) = 2x+4
JA
Answered by Joao A. • Maths tutor
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What is de Moivre's theorem?

de Moivre worked out a brilliant and beautiful way to solve complex equations. If you for example have z 3 = 1 and you want to find all real and complex z that satisfy this equation. i is just a complex numb...
FD
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