Given that y = cos(3x)cosec(5x), use the product rule to find dy/dx.
Write out the product rule: if y=f(x)g(x) where f and g are functions, dy/dx = f'(x)g(x) + f(x)g'(x)
Substitute in the expressions from the question:Therefore if f(x)=cos(3x) and g(x) = cosec(5x), f'(x) = -3sin(3x) and g'(x) = -5cosec(5x)cot(5x)
Solve the question: It follows that if y=f(x)g(x), then dy/dx = -3sin(3x)cosec(5x) - 5cos(3x)cosec(5x)cot(5x) or equivalently dy/dx = -3sin(3x)/sin(5x) - 5cos(3x)cos(5x)/sin^2(5x)
HL
Related Maths A Level answers
All answers ▸A curve with equation y = f(x) passes through the point (4,25). Given that f'(x) = (3/8)*x^2 - 10x^(-1/2) + 1, find f(x).
y =(4x)/(x^2+5) (a) Find dy/dx, writing your answer as a single fraction in its simplest form. (b) Hence find the set of values of x for which dy/dx<0
What is a stationary point on a curve? How do I calculate the co-ordinates of a stationary point?
How can I find the equation of a line l which passes through the points (5,7) and (3, -1)