Question

2.1. Find the derivatives of the following function using product rule or quotient rule: 2.1. Find the derivatives of the following function using product rule or quotient rule: \text { 2.1.1. } h(z)=\left(1+2 z+3 z^{2}\right)\left(5 z+8 z^{2}-z^{3}\right) \text { with respect to } z \text { 2.1.2. } g(x)=6 x^{2} /(2-x) \text { with respect to } x \text { 2.1.3. } R(w)=\left(3 w+w^{4}\right) /\left(2 w^{2}+1\right) \text { with respect to } w \text { 2.1.4. Find the equation of the tangent line to } f(x)=(1+12 \sqrt{x})\left(4-x^{2}\right) \text { at } x=10 2.1.5. Determine the maximum value of the function f (x) = (x – x²)/(1 + 8x?) and thevalue of x at which this occurs.

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