An equation is formed of two equal expressions. The derivative of the equation y=(2x+1)⁵(x²-1)⁻⁴ is [-2(2x+1)⁴(3x²+4x+5)/(x²-1)⁵].
What is an equation?
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given the equation y=(2x+1)⁵(x²-1)⁻⁴, then the differentiation will be,
[tex]\dfrac{dy}{dx}=(2x+1)^5(x^2-1)^{-4}[/tex]
[tex]= \dfrac{10\left(2x+1\right)^4\left(x^2-1\right)^4-8x\cdot\left(2x+1\right)^5\left(x^2-1\right)^3}{\left(x^2-1\right)^8}[/tex]
[tex]=\dfrac{10\left(2x+1\right)^4}{\left(x^2-1\right)^4}-\dfrac{8x\cdot\left(2x+1\right)^5}{\left(x^2-1\right)^5}[/tex]
[tex]= -\dfrac{2\left(2x+1\right)^4\left(3x^2+4x+5\right)}{\left(x^2-1\right)^5}[/tex]
Hence, the derivative of the equation y=(2x+1)⁵(x²-1)⁻⁴ is [-2(2x+1)⁴(3x²+4x+5)/(x²-1)⁵].
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