Dê a derivada de :Y= X^4/4X^3/3+5X^2/4+1/X-2

Dada a equação \(y={1 \over 4}x^4 + {1 \over 3}x^3 + {5 \over 4}x^2+{1 \over x} - 2\), sua derivada é:

\(\Longrightarrow {\partial y \over \partial x}={\partial \over \partial x} \Big ( {1 \over 4}x^4 + {1 \over 3}x^3 + {5 \over 4}x^2+{1 \over x} - 2 \Big )\)

\(\Longrightarrow {\partial y \over \partial x}={\partial \over \partial x} \Big ( {1 \over 4}x^4 + {1 \over 3}x^3 + {5 \over 4}x^2+x^{-1} - 2 \Big )\)

\(\Longrightarrow {\partial y \over \partial x}= {1 \over 4}\cdot 4x^{4-1} + {1 \over 3}\cdot 3x^{3-1} + {5 \over 4}\cdot 2x^{2-1}+(-1)x^{-1-1} - 0 \)

\(\Longrightarrow {\partial y \over \partial x}= x^{3} + x^{2} + {5 \over 2} x - x^{-2}\)

\(\Longrightarrow \fbox {$ {\partial y \over \partial x}= x^{3} + x^{2} + {5 \over 2} x - {1 \over x^{2} } $}\)