find $\frac{dy}{dx}$.

\y = \frac{6}{\cos x} + \frac{7}{\tan x}\

$\frac{dy}{dx} = \square$

Question

find $\frac{dy}{dx}$.

\y = \frac{6}{\cos x} + \frac{7}{\tan x}\

$\frac{dy}{dx} = \square$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Trigonometric Derivatives" ], "new_concepts": [], "current_concepts": [ "Trigonometric Derivatives", "Quotient Rule" ] } ## Rewrite the function using reciprocal trigonometric identities $$ y = 6\sec(x) + 7\cot(x) $$ ## Differentiate each term with respect to x $$ \begin{aligned} \frac{d}{dx}[6\sec(x)] &= 6\sec(x)\tan(x) \ \frac{d}{dx}[7\cot(x)] &= -7\csc^2(x) \end{aligned} $$ ## Combine the derivatives $$ \frac{dy}{dx} = 6\sec(x)\tan(x) - 7\csc^2(x) $$ $\frac{dy}{dx} =$ $6\sec(x)\tan(x) - 7\csc^2(x)$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Calculus", "Trigonometric Derivatives" ] }

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QUESTION IMAGE

Question

Explanation:

Rewrite the function using reciprocal trigonometric identities

Differentiate each term with respect to x

Combine the derivatives

Answer: