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1 of 8
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Differentiate a composite function by the chain rule
DIFFICULTY
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standard
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Question 1 of 8
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Use the displayed function rule
\[y=\left(-3\,z - 5\right)^{\frac{3}{2}}\]
1 mark
Find the derivative of the displayed function
\[\frac{dy}{dz}=-3\]
\[\frac{dy}{dz}=\frac{3}{2}\,z^{\frac{1}{2}}\,\left(-3\right)\]
\[\frac{dy}{dz}=\frac{3}{2}\,\left(-3\,z - 5\right)^{\frac{1}{2}}\]
\[\frac{dy}{dz}=\frac{3}{2}\,\left(-3\,z - 5\right)^{\frac{1}{2}}\,\left(-3\right)\]
CHECK
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