Differentate sin(x^2+1) with respect to x
y = sin(x2+1) In general, the chain rule is: dy/dx = f(g(x)) = df/dg * dg/dx Applying this to y: dy/dx = d(sin(x2+1))/d(x2+1) * d(x2+1)/dx = cos(x2+1) * (2x) = 2xcos(x2+1)
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The straight line with equation y=3x-7 does not cross or touch the curve with equation y=2px^2-6px+4p, where p is a constant.(a) Show that 4p^2-20p+9<0 (b) Hence find the set of possible values for p.
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In a triangle ABC, side AB=10 cm, side AC=5cm and the angle BAC=θ, measured in degrees. The area of triangle ABC is 15cm(sq). Find 2 possible values for cosθ and the exact length of BC, given that it is the longest side of the triangle.