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Question Number 155365 by MathsFan last updated on 29/Sep/21

$$y=\frac{10}{{(2x^2+1)}^5}$$$$find\frac{dy}{dx}$$

Answered by gsk2684 last updated on 29/Sep/21

$$10\left(\frac{-5}{{(2x^2+1)}^6}\right)(2\left(2x\right)+0)$$$$\frac{-200x}{{(2x^2+1)}^6}$$

Commented by MathsFan last updated on 29/Sep/21

$$correctsir$$

Answered by peter frank last updated on 29/Sep/21

$$\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\underset{―}{{({2\mathrm{x}}^2+1)}^5\frac{\mathrm{d}}{\mathrm{dx}}\left(10\right)-10\frac{\mathrm{d}}{\mathrm{dx}}{({2\mathrm{x}}^2+1)}^5}}{{\left[{({2\mathrm{x}}^2+1)}^5\right]}^2}$$$$\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{-10.5.{({2\mathrm{x}}^2+5)}^4.4\mathrm{x}}{{({2\mathrm{x}}^2+1)}^{10}}$$$$\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{-200\mathrm{x}}{{({2\mathrm{x}}^2+1)}^6}$$

Commented by MathsFan last updated on 29/Sep/21

$$thankyou$$

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