Solve for: y=2x^5-5x^{-4}+8x^2-11x

Expression: $y=2{x}^{5}-5{x}^{-4}+8{x}^{2}-11x$

Take the derivative of both sides

$y '=\frac{ \mathrm{d} }{ \mathrm{d}x} \left( 2{x}^{5}-5{x}^{-4}+8{x}^{2}-11x \right)$

Use differentiation rule $\frac{ \mathrm{d} }{ \mathrm{d}x} \left( f+g \right)=\frac{ \mathrm{d} }{ \mathrm{d}x} \left( f \right)+\frac{ \mathrm{d} }{ \mathrm{d}x} \left( g \right)$

$y '=\frac{ \mathrm{d} }{ \mathrm{d}x} \left( 2{x}^{5} \right)+\frac{ \mathrm{d} }{ \mathrm{d}x} \left( -5{x}^{-4} \right)+\frac{ \mathrm{d} }{ \mathrm{d}x} \left( 8{x}^{2} \right)+\frac{ \mathrm{d} }{ \mathrm{d}x} \left( -11x \right)$

Find the derivative

$y '=2 \times 5{x}^{4}+\frac{ \mathrm{d} }{ \mathrm{d}x} \left( -5{x}^{-4} \right)+\frac{ \mathrm{d} }{ \mathrm{d}x} \left( 8{x}^{2} \right)+\frac{ \mathrm{d} }{ \mathrm{d}x} \left( -11x \right)$

Find the derivative

$y '=2 \times 5{x}^{4}-5 \times \left( -4{x}^{-5} \right)+\frac{ \mathrm{d} }{ \mathrm{d}x} \left( 8{x}^{2} \right)+\frac{ \mathrm{d} }{ \mathrm{d}x} \left( -11x \right)$

Find the derivative

$y '=2 \times 5{x}^{4}-5 \times \left( -4{x}^{-5} \right)+8 \times 2x+\frac{ \mathrm{d} }{ \mathrm{d}x} \left( -11x \right)$

Find the derivative

$y '=2 \times 5{x}^{4}-5 \times \left( -4{x}^{-5} \right)+8 \times 2x-11$

Simplify the expression

$y '=10{x}^{4}+\frac{ 20 }{ {x}^{5} }+16x-11$