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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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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 c...

Answered by Alexander B. • Maths tutor

10789 Views

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

Answered by Leila G. • Biology tutor

4170 Views

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

8524 Views

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 =...

Answered by Paolo F. • Physics tutor

8571 Views