Solve f(x,y)=(x-1)(y-1)*x^2y^2 - ScanMath

HOME CALCULATOR

DOWNLOAD FOR FREE

Algebra
Calculus
Trigonometry
Matrix

Type your math problem... f(x,y)=(x-1)(y-1)*x^2y^2

Question

Function

Find the first partial derivative with respect to x

solver-selected-icon

Find the first partial derivative with respect to y

f_{x} = 3 y^{3} x^{2} - 3 x^{2} y^{2} - 2 x y^{3} + 2 x y^{2}

Simplify

f (x, y) = (x - 1) (y - 1) x^{2} y^{2}

Find the first partial derivative by treating the variable y as a constant and differentiating with respect to x

f_{x} = \frac{\partial}{\partial x} ((x - 1) (y - 1) x^{2} y^{2})

Use differentiation rule \frac{\partial}{\partial x} (f (x) \times g (x)) = \frac{\partial}{\partial x} (f (x)) \times g (x) + f (x) \times \frac{\partial}{\partial x} (g (x))

f_{x} = \frac{\partial}{\partial x} (x - 1) (y - 1) x^{2} y^{2} + (x - 1) \times \frac{\partial}{\partial x} (y - 1) x^{2} y^{2} + (x - 1) (y - 1) \times \frac{\partial}{\partial x} (x^{2}) y^{2} + (x - 1) (y - 1) x^{2} \times \frac{\partial}{\partial x} (y^{2})

Evaluate

More Steps

f_{x} = 1 \times (y - 1) x^{2} y^{2} + (x - 1) \times \frac{\partial}{\partial x} (y - 1) x^{2} y^{2} + (x - 1) (y - 1) \times \frac{\partial}{\partial x} (x^{2}) y^{2} + (x - 1) (y - 1) x^{2} \times \frac{\partial}{\partial x} (y^{2})

Evaluate

f_{x} = y^{3} x^{2} - x^{2} y^{2} + (x - 1) \times \frac{\partial}{\partial x} (y - 1) x^{2} y^{2} + (x - 1) (y - 1) \times \frac{\partial}{\partial x} (x^{2}) y^{2} + (x - 1) (y - 1) x^{2} \times \frac{\partial}{\partial x} (y^{2})

Use \frac{\partial}{\partial x} (c) = 0 to find derivative

f_{x} = y^{3} x^{2} - x^{2} y^{2} + (x - 1) \times 0 \times x^{2} y^{2} + (x - 1) (y - 1) \times \frac{\partial}{\partial x} (x^{2}) y^{2} + (x - 1) (y - 1) x^{2} \times \frac{\partial}{\partial x} (y^{2})

Evaluate

f_{x} = y^{3} x^{2} - x^{2} y^{2} + 0 + (x - 1) (y - 1) \times \frac{\partial}{\partial x} (x^{2}) y^{2} + (x - 1) (y - 1) x^{2} \times \frac{\partial}{\partial x} (y^{2})

Use \frac{\partial}{\partial x} x^{n} = n x^{n - 1} to find derivative

f_{x} = y^{3} x^{2} - x^{2} y^{2} + 0 + (x - 1) (y - 1) \times 2 x y^{2} + (x - 1) (y - 1) x^{2} \times \frac{\partial}{\partial x} (y^{2})

Evaluate

f_{x} = y^{3} x^{2} - x^{2} y^{2} + 0 + 2 x^{2} y^{3} - 2 x^{2} y^{2} - 2 x y^{3} + 2 x y^{2} + (x - 1) (y - 1) x^{2} \times \frac{\partial}{\partial x} (y^{2})

Use \frac{\partial}{\partial x} (c) = 0 to find derivative

f_{x} = y^{3} x^{2} - x^{2} y^{2} + 0 + 2 x^{2} y^{3} - 2 x^{2} y^{2} - 2 x y^{3} + 2 x y^{2} + (x - 1) (y - 1) x^{2} \times 0

Evaluate

f_{x} = y^{3} x^{2} - x^{2} y^{2} + 0 + 2 x^{2} y^{3} - 2 x^{2} y^{2} - 2 x y^{3} + 2 x y^{2} + 0

Removing 0 doesn't change the value,so remove it from the expression

f_{x} = y^{3} x^{2} - x^{2} y^{2} + 2 x^{2} y^{3} - 2 x^{2} y^{2} - 2 x y^{3} + 2 x y^{2}

Add the terms

More Steps

f_{x} = 3 y^{3} x^{2} - x^{2} y^{2} - 2 x^{2} y^{2} - 2 x y^{3} + 2 x y^{2}

Solution

More Steps

f_{x} = 3 y^{3} x^{2} - 3 x^{2} y^{2} - 2 x y^{3} + 2 x y^{2}

Show Solution