What is (\partial)/(\partial y)(Tx^5y^4z^8) ?

The answer to (\partial)/(\partial y)(Tx^5y^4z^8) is 4Tx^5y^3z^8

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(\partial)/(\partial y)(Tx^5y^4z^8)

\frac{\partial}{\partial y} (T x^{5} y^{4} z^{8})

4 T x^{5} y^{3} z^{8}

Solution steps

\frac{\partial}{\partial y} (T x^{5} y^{4} z^{8})

Treat

T, x, z

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= T x^{5} z^{8} \frac{\partial}{\partial y} (y^{4})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= T x^{5} z^{8} \cdot 4 y^{4 - 1}

Simplify

= 4 T x^{5} y^{3} z^{8}

\frac{x ^{2}}{x ^{3} - 3 x}, \frac{1}{x ^{3} - 3 x}, 2, 11

\frac{d}{d x} (\frac{x e ^{x}}{sin ( x ) + 1})

tan^{2} (3 x)

y = 6 x^{3} ln (5 x)

\frac{x}{2}, 4

What is (\partial)/(\partial y)(Tx^5y^4z^8) ?
The answer to (\partial)/(\partial y)(Tx^5y^4z^8) is 4Tx^5y^3z^8