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Apply the formula: $\frac{d}{dx}\left(\frac{a}{b}\right)$$=\frac{\frac{d}{dx}\left(a\right)b-a\frac{d}{dx}\left(b\right)}{b^2}$, where $a=\left(x^5+3x\right)^4$ and $b=\cos\left(x\right)$
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$\frac{\frac{d}{dx}\left(\left(x^5+3x\right)^4\right)\cos\left(x\right)-\left(x^5+3x\right)^4\frac{d}{dx}\left(\cos\left(x\right)\right)}{\cos\left(x\right)^2}$
Learn how to solve problems step by step online. Find the derivative d/dx(((x^5+3x)^4)/cos(x)). Apply the formula: \frac{d}{dx}\left(\frac{a}{b}\right)=\frac{\frac{d}{dx}\left(a\right)b-a\frac{d}{dx}\left(b\right)}{b^2}, where a=\left(x^5+3x\right)^4 and b=\cos\left(x\right). Apply the formula: \frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}\frac{d}{dx}\left(x\right), where a=4 and x=x^5+3x. Apply the trigonometric identity: \frac{d}{dx}\left(\cos\left(\theta \right)\right)=-\sin\left(\theta \right). Apply the formula: 1x=x, where x=\left(x^5+3x\right)^4\sin\left(x\right).
