Math  /  Trigonometry

QuestionMatch each trigonometric function with its derivative by entering the correct letter in the gi A. y=tan(7x)y=\tan (7 x) B. y=tan(x7)y=\tan \left(x^{7}\right) dydx=sec2(x7)\frac{d y}{d x}=\sec ^{2}\left(x^{7}\right) C. y=cot7(x)y=\cot ^{7}(x) dydx=7cot6(x)csc(x)\frac{d y}{d x}=-7 \cot ^{6}(x) \csc (x) dydx=7x6sec2(x7)\frac{d y}{d x}=7 x^{6} \sec ^{2}\left(x^{7}\right) D. y=7cot(x)y=7 \cot (x) dydx=7cot6(x)csc2(x)\frac{d y}{d x}=-7 \cot ^{6}(x) \csc ^{2}(x) E. Not the derivative of A,B,CA, B, C, or DD. dydx=7csc2(x)dydx=7sec2(7x)\begin{array}{l} \frac{d y}{d x}=-7 \csc ^{2}(x) \\ \frac{d y}{d x}=7 \sec ^{2}(7 x) \end{array}

Studdy Solution
Identify any derivatives that do not match any function:
- The derivative dydx=sec2(x7) \frac{dy}{dx} = \sec^2(x^7) does not match any of the given functions A, B, C, or D.
The matches are: - A matches with dydx=7sec2(7x) \frac{dy}{dx} = 7 \sec^2(7x) . - B matches with dydx=7x6sec2(x7) \frac{dy}{dx} = 7x^6 \sec^2(x^7) . - C matches with dydx=7cot6(x)csc2(x) \frac{dy}{dx} = -7 \cot^6(x) \csc^2(x) . - D matches with dydx=7csc2(x) \frac{dy}{dx} = -7 \csc^2(x) . - E corresponds to dydx=sec2(x7) \frac{dy}{dx} = \sec^2(x^7) .

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