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A curve has the equation x^2+2y^2=3x, by differentiating implicitly find dy/dy in terms of x and y.

We shall differentiate each term in the equation with respect to x. dy/dx (x 2 ) = 2x dy/dx (2y 2 ) = 4y dy/dx dy/dx (3x) = 3 So we now have the equation 2x + 4y dy/dx =3 We now have to rearrange to get in t...
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Answered by Kate P. • Maths tutor
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Solve e^x-6e^-x=1

Multiply everything through by e x and rearrange so it equals zero you now have e 2x -e x -6=0 It is now similar to a quadratic equation, make the dummy substitution y=e x y=3 or -2 x= ln(3) and ln(-2) does ...
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Answered by Kishwar I. • Maths tutor
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Consider a differential equation where dx/dt = -axt. Find an equation for x(t).

Starting from dx/dt = -axt. We treat dx and dt as infinitessimal factors of x and t, therefore fundemental mathematical operations still apply. Rearranging the equation to group x, dx and t, dt. 1/x dx = -at...
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Answered by Cal L. • Maths tutor
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How do you differentiate a function comprised of two functions multiplied together?

The product rule is useful when you’re dealing with a function comprised of two functions multiplied together. Generally, if you have a function of the form y = f(x)g(x), then the derivative of the function ...
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Answered by Elliot G. • Maths tutor
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the graph y = 3/((1-4x)*(1/2)) has a shaded region between x = 0 and x = 2, find area of the region

intergrate y with respect to x between x=0 and x=2. remove 3 from the numerator, take outside intergration intergrate normally answer = 3
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Answered by Charlie N. • Maths tutor
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