What is the derivative of (1+x^3Y^2Z^2) ?

The derivative of (1+x^3Y^2Z^2) is 6x^2Y^2Z(1+x^3Y^2Z)

What is the first derivative of (1+x^3Y^2Z^2) ?

The first derivative of (1+x^3Y^2Z^2) is 6x^2Y^2Z(1+x^3Y^2Z)

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\frac{d}{d x} ((1 + x^{3} Y^{2} Z)^{2})

6 x^{2} Y^{2} Z (1 + x^{3} Y^{2} Z)

Solution steps

\frac{d}{d x} ((1 + x^{3} Y^{2} Z)^{2})

Treat

Y, Z

as constants

Apply the chain rule:

2 (1 + x^{3} Y^{2} Z) \frac{d}{d x} (1 + x^{3} Y^{2} Z)

= 2 (1 + x^{3} Y^{2} Z) \frac{d}{d x} (1 + x^{3} Y^{2} Z)

\frac{d}{d x} (1 + x^{3} Y^{2} Z) = 3 Y^{2} Z x^{2}

= 2 (1 + x^{3} Y^{2} Z) \cdot 3 Y^{2} Z x^{2}

Simplify

= 6 x^{2} Y^{2} Z (1 + x^{3} Y^{2} Z)

\frac{d}{d x} (4^{x} ln (4))

y^{^{'}} (y - x^{2}) = - 2 y

\frac{\partial}{\partial x} (ln (x^{4} + y^{2}))

y^{^{'}} = 7 x + y, y (0) = 8

y = x^{3}, y = 3 x + 2

What is the derivative of (1+x^3Y^2Z^2) ?
The derivative of (1+x^3Y^2Z^2) is 6x^2Y^2Z(1+x^3Y^2Z)
What is the first derivative of (1+x^3Y^2Z^2) ?
The first derivative of (1+x^3Y^2Z^2) is 6x^2Y^2Z(1+x^3Y^2Z)