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Maths
A Level

Differentiate y = (sin(x))^2 (find dy/dx)

This a relatively simple question which requires the use of the chain rule to solve. First we set u = sin(x)  so we then have y = u. Next we perform do differentiations, one on u as a functio...

TC
Answered by Tabraiz C. Maths tutor
16212 Views

Solve these simultaneous equations: 2x+y-5=0 and x^2-y^2=3

To solve this problem, you need to: rearrange the first equation (1) to express y in terms of x to obtain equation (3). Then, substitute this new equation into the quadratic one (the second equation from ...

NB
Answered by Nana B. Maths tutor
5226 Views

What is the integral of sin(3x) cos(5x)?

Using trig formulas we have sin(5x+3x)= sin(5x)cos(3x)+cos(5x)sin(3x) and sin(5x-3x)= sin(5x)cos(3x) - cos(5x)sin(3x). Hence, sin(5x+3x) - sin(5x-3x) = sin(8x)-sin(2x) = 2cos(5x)sin(3x). This implies that...

MN
Answered by Morenikeji N. Maths tutor
5870 Views

solve 4^xe^(7x+5) = 21

ln((4^x)e^(7x+5)) = ln21; apply a natural log on both sides of the equation as an exponential containing e is involved 

ln4^x + ln(e^(7x+5)) = ln21; using logarithm rules you can seperate the singl...

WN
Answered by Wahib N. Maths tutor
3470 Views

How do you integrate y = 4x^3 - 5/x^2?

First we should look at the formula for integrating xn. The integral is (xn+1 / n+1) + C.

Let's break down our equation into two parts. 

  1. The integral of 4x

    HJ
    Answered by Hannah J. Maths tutor
    4960 Views

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