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Given that y = (3x^4 + x)^5, find dy/dx using the chain rule.

Let u = 3 x 4 + x du/dx = 12x 3 + 1 y = u 5 dy/du = 5u 4 Using the chain rule, dy/dx = dy/du x du/dx = 5 u 4 (12x 3 + 1) dy/dx = 5(3x 4 + x)(12x 3 +1)
Answered by • Maths tutor
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Given that f(x)= (4/x) - 3x + 2 find i) f'(x) and ii) f''(1/2)

This question is asking us to find the first order derivative of f(x) with respect to x, then the second order derivative when x=1/2i) Firstly, let's consider (d/dx)4/x:There are two ways to think about diff...
VB
Answered by Verity B. • Maths tutor
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Show me why the product of a squared and a cubed is a to the power of 5.

When we find the product of two terms that has the same base (in this case, a), we can simply add the powers. This can be explained using knowledge of squares and cubed. a 2 = a x a and a 3 = a x a x a and s...
LM
Answered by Leon M. • Maths tutor
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expand (x-3)^2

firstly explain (x-3) 2 = (x-3)(x-3) on the whiteboard I'd draw a square grid with each of the numbers, then I'd multiply out. E.g. x multiplied by x = x 2 ; x multiplied by -3 = -3x and so on.. (remembering...
IT
Answered by Imogen T. • Maths tutor
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2x + 7y = 14 and x + y = 2. Find the value of x and y which satisfy both equations.

There are 2 ways to solve simultaneous equations which are by substitution or elimination. In this example you can use both but elimination is simpler. So we have 2x + 7y = 14 and x + y = 2. To use eliminati...
AS
Answered by Amir S. • Maths tutor
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