If {eq}z = x^2y - y^2\sin^{-1} x {/eq}, find {eq}\dfrac {\partial z}{\partial y} {/eq} at {eq}(1, 2) {/eq}.
Question:
If {eq}z = x^2y - y^2\sin^{-1} x {/eq}, find {eq}\dfrac {\partial z}{\partial y} {/eq} at {eq}(1, 2) {/eq}.
Partial derivatives:
Partial derivative to a function containing more than one variable is the derivative of that function with respect to a single variable, i.e., Other variables are treated as a constant that do not vary.
Answer and Explanation: 1
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We have,
$$z = x^2y - y^2\sin^{-1} x $$
Differentiate t{eq}z {/eq} with respect to {eq}y {/eq}, treat the variable {eq}x {/eq} as a constant,
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The Chain Rule for Partial Derivatives
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Chapter 14 / Lesson 4
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This lesson defines the chain rule. It goes on to explore the chain rule with partial derivatives and integrals of partial derivatives.
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