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Differentiate z = e^(3y^2+5) with respect to y. (Hint: use chain rule.)

We can find dz/dy using chain rule dz/dy=dz/du x du/dy (1) by defining u=3y^2+5 (since the exponent of e is a function of y we call this function u) and rewrite z=e^u. Then, we find dz/du=e^u (2) and du/dy=6...
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Answered by Sophie H. • Maths tutor
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Given y = 4x/(x^2 +5) find dy/dx, writing your answer as a single fraction in its simplest form

This function is fraction so the easiest method is to use the quotient rule (though the product rule can be used). Recall the quotient rule dy/dx = [vu' - uv']/[v^2]Note, u and v refer to the numerator and d...
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Answered by Laurence C. • Maths tutor
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The equation of the line L1 is y = 3x – 2. The equation of the line L2 is 3y – 9x + 5 = 0. Show that these two lines are parallel.

To begin with,for every line ax+by+c=0 the gradient is m=(-a)/b.From theory, it is known that two lines are parallel only if their gradients are equal. For line 1: y=3x-2, it implies that 3x-y-2=0(we just su...
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Answered by Anca I. • Maths tutor
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How do you factorise a quadratic equation?

By looking at the equation you see it is made up of three components. The way to factorise it is to multiply the integer or constant at the end by the coefficient of the x 2 term, the number before the x 2 ....
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Answered by Sidhi K. • Maths tutor
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Expand and simplify 9(x+3)-2(3x-4)

9(x+3)-2(3x-4)9x+27-6x+83x+35
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Answered by Kiran S. • Maths tutor
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