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Using the quotient rule: Let u=x and v=2x+5 then du/dx= 1 and dv/dx=2 Hence dy/dx=[(2x+5)x1- (2x)]/(2x+5)²             =5/(2x+5)²

First, you must find out the total amount to pay back, this amount will be £720 + 15% of £720. To find 15% of £720, we first calculate 720/100 to find 1% and the multiply by 15: 720/100 = 7.2 *15 = 108. N...

Integrate by parts: integral = [uv] - ∫u'v dx (u'= derivative of u, v'= derivative of v)

u= x     u'= 1

v' = sin2x        v= -0.5cos2x

= -0.5xcosx  -  ∫-0.5cos2x dx

= -0.5xcosx...

Integrate, y= 3x² -1/x

 1{³ 3x² - 1/x dx = [x-lnx]³₁= (3-ln3)-(1-ln1) = 3-ln3-1+0= 2-ln3

First of all, let's start by defining the word 'interest'. Interest in mathematical terms generally means an amount of money that is accumulated over a period of time after an amount of money is invested ...