1 of 8 0-day streak

Differentiate a product or quotient of two functions

Question 1 of 8

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A function is defined as follows

q(s)=\left(-5\,s\right)\left(2\,\cos\left(2\,s\right)\right)

u(s)=-5\,s

v(s)=2\,\cos\left(2\,s\right)

(a)1 mark

Which method should be used first for the displayed expression?

Apply the quotient rule

Apply the product rule

Simplify the expression exactly before differentiating

(b)8 marks

Complete the table for the two factors and their derivatives. Enter every value in exact form

u coefficient u exponent u' coefficient u' exponent v coefficient v rate v' coefficient v' rate

Differentiate the function and select the correct next line

q'(s)=\left(-5\right)\left(-5\,s\right) + \left(-4\,\sin\left(2\,s\right)\right)\left(2\,\cos\left(2\,s\right)\right)

q'(s)=\left(-5\right)\left(2\,\cos\left(2\,s\right)\right)

q'(s)=\left(-5\right)\left(2\,\cos\left(2\,s\right)\right) + \left(-5\,s\right)\left(-4\,\sin\left(2\,s\right)\right)

q'(s)=\left(-5\,s\right)\left(-4\,\sin\left(2\,s\right)\right)