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y = (x^2)sin(3x). Find dy/dx

We need to differentiate x 2 sin(3x). We know how to differentiate (x 2 ) on its own, and how to differentiate sin(3x) on its own. So we can use the Product rule: dy/dx = (d/dx(x 2 ))sin(3x) + x 2 (d/dx(sin(...
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Answered by Robert D. • Maths tutor
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differentiate x^2 + y^3 + xy respect to x

2x + 3y 2 * dy/dx + x * dy/dx +y
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Answered by Xianming J. • Maths tutor
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dx/dt=-5x/2 t>=0 when x=60 t=0

dx/dt=-5x/2 Int(x, dx)=Int(-5/2, dt) ln(x)=-5t/2+c x=60 when t=0 ln(60)=c ln(x)=ln(60)-5t/2 x=e ln(60)-5t/2 x=60/e 5t/2
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Answered by Felix D. • Maths tutor
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Given that sin(x)^2 + cos(x)^2 = 1, show that sec(x)^2 - tan(x)^2 = 1 (2 marks). Hence solve for x: tan(x)^2 + cos(x) = 1, x ≠ (2n + 1)π and -2π < x =< 2π(3 marks)

sin(x) 2 + cos(x) 2 = 1 Dividing by cos(x) 2 gives: tan(x) 2 + 1 = sec(x) 2 Which rearranges as: sec(x) 2 - tan(x) 2 = 1 as required. tan(x) 2 + cos(x) 2 = 1 sec(x) 2 - 1 + cos(x) 2 = 1 sec(x) 2 + cos(x) 2 =...
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Answered by Alistair R. • Maths tutor
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Solve for 0 =< x =< 360 16/(cos(x+25)+1) = 10, give answers to 2 d.p.

Rearrange to get cos(x+25) = 0.6 Use inverse cosine to get (x+25) = -53.13... 53.13... 306.86... 413.13... Isolate x to get x = -78.13... 28.13... 281.86... 388.13... Apply the limits and round the answers t...
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Answered by Barnaby W. • Maths tutor
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