Answer to Question #194251 in Calculus for Maureen

Question #194251

Use the technique of differentiation to find dy over dx

Y=(xcube+7xsquared-8) (2x to the power -3 + x to the power -4)


1
Expert's answer
2021-05-18T08:02:02-0400

y=(x3+7x28)(2x3+x4)differentiate w.r.t x,y=(x3+7x28)(6x44x5)+(2x3+x4)(3x2+14x)=6x14x242x228x3+48x4+32x5+6x1+28x2+3x2+14x3=15x214x3+48x4+32x5y=(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 \newline


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