Studdy AI Logo
Math  /  Calculus

Questiona. Use the product rule to find the derivative of the given function. b. Find the derivative by expanding the product first. h(z)=(4−z2)(z3−2z+5)h(z)=\left(4-z^{2}\right)\left(z^{3}-2 z+5\right) a. Use the product rule to find the derivative of the given function. Select the correct answer below and fill in the answer box(es) to complete your choice. A. The derivative is (4−z2)(z3−2z+5)\left(4-z^{2}\right)\left(z^{3}-2 z+5\right) □\square ). B. The derivative is (z3−2z+5)\left(z^{3}-2 z+5\right) □\square ). C. The derivative is (4−z2)(□)\left(4-z^{2}\right)(\square). D. The derivative is (4−z2)(□)+(z3−2z+5)(□)\left(4-z^{2}\right)(\square)+\left(z^{3}-2 z+5\right)(\square). E. The derivative is (4−z2)(z3−2z+5)+(□)\left(4-z^{2}\right)\left(z^{3}-2 z+5\right)+(\square).

Studdy Solution
Confirm that both results are consistent:
Both methods yield the same derivative:
h′(z)=−5z4+18z2−10z−8 h'(z) = -5z^4 + 18z^2 - 10z - 8
Hence, the correct answer for part (a) is:
D. The derivative is (4−z2)(3z2−2)+(z3−2z+5)(−2z)(4 - z^2)(3z^2 - 2) + (z^3 - 2z + 5)(-2z).
Hence:
h′(z)=(4−z2)(3z2−2)+(z3−2z+5)(−2z) h'(z) = (4 - z^2)(3z^2 - 2) + (z^3 - 2z + 5)(-2z)

View Full Solution - Free
Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord