Find dxdy, if x32+y32=a32
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Step-by-Step Solution
Step 1: Differentiate implicitly
To find dxdy, we need to differentiate both sides of the given equation with respect to x. Since y is a function of x, we will use the chain rule for the term involving y. The term a32 is a constant, so its derivative will be zero.
Step 2: Apply power rule and chain rule
Applying the power rule, dxd(xn)=nxn−1, to x32 gives 32x−31. For y32, we use the chain rule, which results in 32y−31dxdy. The derivative of the constant a32 is 0.
Step 3: Simplify the exponents
We simplify the exponents: 32−1=−31. This gives us the simplified form of the differentiated equation.
Step 4: Isolate dxdy term
To solve for dxdy, we first move the term not containing dxdy to the right side of the equation.
Step 5: Solve for dxdy
Divide both sides by 32y−31 to solve for dxdy. We can then simplify the expression using the property a−n=an1 and an1=na.