Question

(x^2-3)(x^3+5x) find the derivatives of following.​

Answer 1

$( {x}^{2} - 3)( {x}^{3} + 5x) \\ first \: simplify \: this \: or \: apply \: multiplication \: rule \\ {x}^{5} + 5 {x}^{3} - 3 {x}^{3} - 15x \\ {x}^{5} + 2 {x}^{3} - 15x \\ apply \: nx {}^{n - 1} \\ \frac{d(x {}^{5} + 2 {x}^{ 3} - 15x)}{dx} \\ \frac{d( {x}^{5} )}{dx} + \frac{d(2 {x}^{3}) }{dx} - \frac{d(15x)}{dx} \\ 5(x {}^{5 - 1} ) + 3(2 {x}^{3 - 1} ) - 1(15x {}^{1 - 1} ) \\ 5 x{ }^{4} + 6 {x}^{2} - 15$

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