Answered

Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Explore a wealth of knowledge from professionals across different disciplines on our comprehensive platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

I have been struggling with this problem for around 2 hours and can’t seem to get it

I Have Been Struggling With This Problem For Around 2 Hours And Cant Seem To Get It class=

Sagot :

the quotient rule say:

[tex](\frac{f(x)}{g(x)})^{\prime}=\frac{g(x)\cdot f^{\prime}(x)-f(x)\cdot g^{\prime}(x)}{(g(x))^2}[/tex]

now we defined:

[tex]\begin{gathered} f(x)=-4x^2+16 \\ g(x)=(x^2+4)^2 \end{gathered}[/tex]

and the derivative:

[tex]\begin{gathered} f^{\prime}(x)=-8x \\ g^{\prime}(x)=2\cdot(x^2+4)\cdot2x \\ g^{\prime}(x)=4x(x^2+4) \end{gathered}[/tex]

so now we can replace on the quotient rule:

[tex]\frac{(x^2+4)^2\cdot(-8x)-4x(x^2+4)\cdot(-4x^2+16)}{(x^2+4)^4}[/tex]

now we can use properties, like:

[tex](x^2+4)^2=x^4+8x+16[/tex]

Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.