Question

Compute for the derivative of the function below for x = 1. y=35–√x+6x2−23x3+8

Answer 1

SOLUTION

TO DETERMINE

The derivative of the below function for x = 1

$\sf{y = 35 - \sqrt{x} + 6 {x}^{2} - 23 {x}^{3} + 8 }$

EVALUATION

Here the given function is

$\sf{y = 35 - \sqrt{x} + 6 {x}^{2} - 23 {x}^{3} + 8 }$

$\displaystyle \: \sf{ \implies \: y = 43 - {x}^{ \frac{1}{2} } + 6 {x}^{2} - 23 {x}^{3} }$

Differentiating both sides with respect to x we get

$\displaystyle \: \sf{ \: \frac{dy}{dx} = 0 - \frac{1}{2} {x}^{ \frac{1}{2} - 1} + 6 \times 2 {x}^{2 - 1} - 23 \times 3 {x}^{3 - 1} }$

$\displaystyle \: \sf{ \implies \: \frac{dy}{dx} = - \frac{1}{2} {x}^{ - \frac{1}{2} } + 12x - 69 {x}^{2} }$

Now for x = 1 we have

$\displaystyle \: \sf{ \implies \: \frac{dy}{dx} \bigg| _{x = 1} = - \frac{1}{2} {(1)}^{ - \frac{1}{2} } + 12 \times 1 - 69 \times {(1)}^{2} }$

$\displaystyle \: \sf{ \implies \: \frac{dy}{dx} \bigg| _{x = 1} = - \frac{1}{2} + 12 - 69 }$

$\displaystyle \: \sf{ \implies \: \frac{dy}{dx} \bigg| _{x = 1} = - 57 \frac{1}{2} }$

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