Find dy dx if y=5 x^3+x^2+x-10. - Vidyadip

Question

Find $\frac{ dy }{ dx }$ if $y=5 x^3+x^2+x-10$.

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Answer

Here, $y =5 x ^3+ x ^2+ x -10$
$\left.\therefore \frac{d y}{d x}=\frac{d}{d x}\left(5 x ^3\right)+\frac{1}{2} x ^2+\frac{3}{4} x -10\right)$
$=\frac{d}{d x}\left(5 x^3\right)+\frac{d}{d x}\left(\frac{1}{2} x ^2\right)+\frac{d}{d x}\left(\frac{3}{4} x \right)-\frac{d}{d x}(10)$
$=5 \frac{d}{d x}\left(x^3\right)+\frac{1}{2} \frac{d y}{d x}\left(x^2\right)+\frac{3}{4} \frac{d y}{d x}( x )-\frac{d}{d x}(10)$
$=5\left(3 x^2\right)+\frac{1}{2}(2 x )+\frac{3}{4}(1)-0$
$=15 x ^2+ x +\frac{3}{4}$
$\therefore \frac{d y}{d x}=15 x ^2+ x +\frac{3}{4}$

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