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The volume, V, of water in a tank at time t seconds is given by V = 1/3*t^6 - 2*t^4 + 3*t^2, for t=>0. (i) Find dV/dt

The differential of a function is is rate of range of that function. Therefore to find dV/dt, we are finding the rate of change of the volume per unit time.Recall, in order to differentiate a term, e.g. x a ...
SW
Answered by Samuel W. • Maths tutor
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Differentiate with respect to x: y = xln[2x]

This is an example of a question where we would have to use the product rule for differentiation, because we have two functions multiplied together ( x and ln(2x) ).If we have: y = uv, where u and v are func...
MA
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Given that Y=(x+3)(x+5); find dy/dx

Y=(x+5)(x+3) ............(1)The above expression on the right is a product of two expressions,Hence, product rule differentiation method will be employed as stated below:Y(u,v)=U(x).V(x) .........(2)dy/dx=Ud...
DE
Answered by Dr Edosa O. • Maths tutor
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What is the indefinite integral of ln(x) ?

We can use integration by parts to solve this question. If we look at the formula for Integration by parts: ∫u(dv/dx)dx = uv - ∫ v (du/dx) dx , we see that u must be multiplied by something else so therefore...
DM
Answered by Dawud M. • Maths tutor
5363 Views

How do you prove the chain rule?

Given the problem f(x)=(y+x)^5 we use the chain rule as a tool to find the derivative. However, it is difficult to use effectively in further problems without understanding the mechanics of the function. F(x...
EC
Answered by Ella C. • Maths tutor
4595 Views