ib maths sl product and quotient rules
TRANSCRIPT
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Find if: y = 2 x3 sinx
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Product and quotient rules
By the end of the lesson you will be able to:
• Use the product and quotient rules to find the derivative of functions.
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If f (x) = u(x). v(x) then
f '(x)= u'(x).v(x)+u(x).v'(x)
simpler: (uv)' = u'v+uv'
The product rule
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Find if: y = 2 x3 sin x
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Find if:
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Find if:
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Find if:
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Find if:
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Find for y= ex sin x
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The quotient rule
If then:
simpler:
2
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Find if:
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Find if:
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Find if:
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Find if:
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Differentiate with respect to x:
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Find if:
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Find if:
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Find the equations of the tangent line to the curve y= x cos x at the point where x = π.
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The function has a
horizontal tangent line at x = k. Find k.
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Find the coordinates of the two points on the curve y= sinx ( 2 cos x+1), in the rangewhere the gradient is
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Find the coordinates of the stationary points on the curve in the range 0≤x≤2π.
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Find and classify the stationary points on the curve y= x2ex. Hence sketch the curve.
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Solve book Page 220 Ex 7C