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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
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Answered by Harry D. • Maths tutor
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Work out the value of 5^3-5^2:

The first step would be to consider each of the powers individually, work out their value and then proceed with the subtraction to end up with a result. Firstly, as this question is to be done without a calc...
AB
Answered by Alexander B. • Maths tutor
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Oxygen is exchanged between the blood capillaries and the tissues. Give two ways in which capillaries are adapted for exchanging blood with the tissues.

Thin walls for short diffusion path 2. Narrow, so have a large surface area to volume ratio
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Answered by Leila G. • Biology 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 differe...
EM
Answered by Edward M. • Maths tutor
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An aeroplane lands on the runway with a velocity of 50 m/s and decelerates at 10 m/s^2 to a velocity of 20 m/s. Calculate the distance travelled on the runway.

Firstly, we note that the acceleration is constant, therefore this problem should be tackled with the SUVAT equations. Let's write down the information we have: s we are asked to find this u = 50 m/s v = 20 ...
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Answered by Paolo F. • Physics tutor
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