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We need to differentiate x²sin(3x). We know how to differentiate (x²) on its own, and how to differentiate sin(3x) on its own. So we can use the Product rule:

dy/dx = (d/dx(x<...

2x + 3y² * dy/dx + x * dy/dx +y 

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

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)<...