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Differentiate y=x^4sinx

Firstly, we must recognise that the function is in the form of a product, y=uv, where u and v are functions of x. Therefore, we can use the product rule, dy/dx = u (dv/dx) + v (du/dx). 2) We can write u = x^...
HM
Answered by Holly M. • Maths tutor
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Given that y= 5x^2 + 2x , find dy/dx

5x^2 becomes 2 5x as the 2 comes down and 2x becomes 2 as x becomes 1.dy/dx = 2 5x + 2=10x+2
CD
Answered by Camille D. • Maths tutor
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How do I find the inverse of a function?

To find the inverse of a function you need to rearrange from y= a function in terms of x to x= a function in terms of y and then when you write your answer it's important to set it in the form f^-1(x)= a fun...
NH
Answered by Natalie H. • Maths tutor
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Prove that 2 cot (2x) + tan(x) == cot (x)

(1) Aim to rearrange the right hand side (rhs) to make it look like the left hand side.LHS = 2 cot (2x) + tan (x)(2) Notice that the rhs is only in terms of x, whereas the right has a function involving 2x. ...
JC
Answered by Joseph C. • Maths tutor
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The rate of decay of the mass is modelled by the differential equation dx/dt = -(5/2)x. Given that x = 60 when t = 0, solve the quation for x in terms of t.

(1) Rearrange the equation so that the left hand side is a function of x, and the right hand side is a function of t only.dx/dt = - (5/2) x(1/x)dx = -(5/2)dt(2) Integrate both sidesln(x/A) = -(5/2)t, where A...
JC
Answered by Joseph C. • Maths tutor
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