In each case, find ᵈʸ⁄dₓ.
Problem 1 :
x^{2} + y^{2} = 25
Solution :
x^{2} + y^{2} = 25
Differentiate with respect to x.
Problem 2 :
4x^{3}y^{2} + 3x = 1
Solution :
4x^{3}y^{2} + 3x = 1
Differentiate with respect to x.
Problem 3 :
x^{2}y^{2} + 3xy + y = 0
Solution :
x^{2}y^{2} + 3xy + y = 0
Differentiate with respect to x.
Problem 4 :
ln (x + y) = 5x^{2}
Solution :
ln (x + y) = 5x^{2}
Differentiate with respect to x.
Problem 5 :
e^{y} = xy^{2}
Solution :
e^{y} = xy^{2}
Differentiate with respect to x.
Problem 6 :
sin(x^{2} + y^{2}) = e^{y}
Solution :
sin(x^{2} + y^{2}) = e^{y}
Differentiate with respect to x.
cos(x^{2} + y^{2}) ⋅ (x^{2} + y^{2})' = e^{y}(y)'
Problem 7 :
3y^{2 }- cos y = x^{3}
Solution :
3y^{2 }- cos y = x^{3}
Differentiate with respect to x.
Problem 8 :
sin x = x(1 + tan y)
Solution :
sin x = x(1 + tan y)
sin x = x + xtan y
Differentiate with respect to x.
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