Question:
differentiate (x^4)*(y^3)=(x+y)^7
Answer:
Given
x4 * y4 = (x + y)7
Differentiate w.r.t. y, we get
=> 4x3 *y4 + x4 *4y3 * dy/dx = 7(x + y)6 *(1 + dy/dx)
=> 4x3 *y4 + 4x4 *y3 * dy/dx = 7(x + y)6 + 7(dy/dx)*(x + y)6
=> 4x3 *y4 - 7(x + y)6 = 7(dy/dx)*(x + y)6 - 4x4 *y3 * dy/dx
=> 4x3 *y4 - 7(x + y)6 = {7(x + y)6 - 4x4 *y3 }* dy/dx
=> dy/dx = {7(x + y)6 - 4x4 *y3 }/{4x3 *y4 - 7(x + y)6 }
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