5c^(2)d(9c^(2)d^(2)-4c^(3)d-2)

Distribute Terms: Distribute 5c^2d to each term inside the parentheses. 5c^2d(9c^2d^2) = 45c^4d^3, 5c^2d(-4c^3d) = -20c^5d^2, 5c^2d(-2) = -10c^2d;Combine Results: Combine the results from the distribution. The expression simplifies to 45c^4d^3 - 20c^5d^2 - 10c^2d;

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$5 c^{2} d\left(9 c^{2} d^{2}-4 c^{3} d-2\right)$

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Calculus

Find derivatives of using multiple formulae

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5 c^{2} d\left(9 c^{2} d^{2}-4 c^{3} d-2\right)

Distribute Terms: Distribute $5c^2d$ to each term inside the parentheses. $\newline$ $5c^2d(9c^2d^2) = 45c^4d^3$ , $\newline$ $5c^2d(-4c^3d) = -20c^5d^2$ , $\newline$ $5c^2d(-2) = -10c^2d$ ;
Combine Results: Combine the results from the distribution. $\newline$ The expression simplifies to $45c^4d^3 - 20c^5d^2 - 10c^2d$ ;