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Question
Difficulty Level:

Medium

MCQ

Ali tried to find the derivative of (5x6)7(5 x-6)^{7}. Here is his work:

Step 1: This is a composite function. The inner function is u(x)=5x6{u}({x})=5 {x}-6 and the outer function is w(x)=x7{w}({x})=x^{7}

Step 2: We should use the chain rule:

ddx[w(u(x))]=w(u(x))u(x)\frac{d}{d x}[w(u(x))]=w^{\prime}(u(x)) \cdot u^{\prime}(x)

Step 3: Finding the derivatives of the inner and outer functions:

w(x)=7x6 and u(x)=5w^{\prime}(x)=7 x^{6} \text { and } u^{\prime}(x)=5

Step 4: Putting it all together:

ddx[(5x6)7]=7(5x6)6(5)\frac{d}{d x}[(5 x-6)^{7}]=7(5 x-6)^{6} \cdot(5)

=35(5x6)6=35(5 x-6)^{6}

Is Ali’s work correct? If not, what’s his mistake?

Select all that apply :

Ali’s work is correct.

step 1 is incorrect. Ali had a mistake identifying the inner and the outer functions.

step 2 is incorrect. Ali did not state the correct chain rule.

step 3 is incorrect.Ali did not differentiate x7x^{7} correctly.

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