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Given that y = 4x^5 - 5/(x^2) , x=/=0 , find a)dy/dx b)indefinite integral of y

rewrite as y = 4x^5 - 5x^(-2)

dy/dx = 20x^4 + 10x^(-3)

integral of y = 4x^6 / 6 + 5x^(-1) / 1 + c

simplify: 2/3 x^6 + 5/x

Answered by Harry D. • Maths tutor

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Differentiate with respect to x: i) y=x^3ln(2x) ii) y=(x+sin(2x))^3

i) There first step is to acknowledge the need for both product rule (d(uv)/dx=v.du/dx+u.dv/dx) and chain rule (dz/dx=dz/dy*dy/dx). Here, u=x^3 and v=ln(2x). Therefore, du/dx=3x^2 which is a standard diff...

Answered by Edward M. • Maths tutor

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Differentiate f(x) = (x+3)/(2x-5) using the quotient rule.

For a quotient f(x) = u(x)/v(x), the derivative is f'(x) = (vu'(x) - uv'(x))/v(x)². Applying this to the given function, we find u(x) = x+3 and v(x) = 2x-5. So, u'(x) = 1 and v'(x) = 2...

Answered by Sara R. • Maths tutor

4918 Views

Integrate 2x/(x^2+3) using the substitution u=x^2+3

u=x² + 3

du/dx=2x

dx=du/2x

2x/(x²+3) dx becomes (2x/u) * (du/2x)

the 2x terms cancel out giving 1/u du

this integrates to ln(u)+c becoming ln(x

Answered by Tom S. • Maths tutor

12554 Views

Core 1: Given that y = x^4 + x^2+3. Find dy/dx

First what we need to do is we need to think of what the question is asking us to find. In this case it is dy/dx but what is this. This is the rate of change of y with respect to x. For understanding pur...

Answered by David S. • Maths tutor

2698 Views