Use the technique of differentiation to find dy over dx
Y=(xcube+7xsquared-8) (2x to the power -3 + x to the power -4)
y=(x3+7x2−8)(2x−3+x−4)differentiate w.r.t x,y′=(x3+7x2−8)(−6x−4−4x−5)+(2x−3+x−4)(3x2+14x)=−6x−1−4x−2−42x−2−28x−3+48x−4+32x−5+6x−1+28x−2+3x−2+14x−3=−15x−2−14x−3+48x−4+32x−5y=(x^3+7x^2-8)(2x^{-3}+x^{-4})\newline \text{differentiate w.r.t x,}\newline y'=(x^3+7x^2-8)(-6x^{-4}-4x^{-5})+(2x^{-3}+x^{-4})(3x^2+14x)\newline =-6x^{-1}-4x^{-2}-42x^{-2}-28x^{-3}+48x^{-4}+32x^{-5}+6x^{-1}+28x^{-2}+3x^{-2}+14x^{-3}\newline =-15x^{-2}-14x^{-3}+48x^{-4}+32x^{-5} \newline \newliney=(x3+7x2−8)(2x−3+x−4)differentiate w.r.t x,y′=(x3+7x2−8)(−6x−4−4x−5)+(2x−3+x−4)(3x2+14x)=−6x−1−4x−2−42x−2−28x−3+48x−4+32x−5+6x−1+28x−2+3x−2+14x−3=−15x−2−14x−3+48x−4+32x−5
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