1 of 8 0-day streak

Differentiate a product or quotient of two functions

Question 1 of 8

No calculator

Use the displayed function rule

g(x)=\left(-6\,x^{2}\right)\left(-2\,\sin\left(3\,x\right)\right)

u(x)=-6\,x^{2}

v(x)=-2\,\sin\left(3\,x\right)

(a)1 mark

Which method should be used first for the displayed expression?

Apply the product rule

Apply the quotient 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

Find the derivative form of the displayed function

g'(x)=\left(-12\,x\right)\left(-2\,\sin\left(3\,x\right)\right)

g'(x)=\left(-12\,x\right)\left(-2\,\sin\left(3\,x\right)\right) + \left(-6\,x^{2}\right)\left(-6\,\cos\left(3\,x\right)\right)

g'(x)=\left(-6\,x^{2}\right)\left(-6\,\cos\left(3\,x\right)\right)

g'(x)=\left(-12\,x\right)\left(-6\,x^{2}\right) + \left(-6\,\cos\left(3\,x\right)\right)\left(-2\,\sin\left(3\,x\right)\right)