Question

5. Differentiate with respect to \( x \) : (a) \( \frac{3}{\sin (3 x+\pi)} \) (b) \( \frac{5}{\tan ^{2}(2 x+\pi)} \) (c) \( \frac{2}{\cos ^{3}\left(4 x+\frac{\pi}{2}\right)} \) (d) \( \tan \frac{5}{x^{2}} \) (e) \( \sec ^{2} 3 x \) (f) \( \cot ^{3} 5 x \) (g) \( \frac{\sin x-\cos x}{\sin x+\cos x} \) (h) \( 3 x^{2} \tan ^{2}(x+\pi) \) (i) \( 3 x \cos 5 x-5 x \tan 3 x \)

          5. Differentiate with respect to \( x \) :
(a) \( \frac{3}{\sin (3 x+\pi)} \)
(b) \( \frac{5}{\tan ^{2}(2 x+\pi)} \)
(c) \( \frac{2}{\cos ^{3}\left(4 x+\frac{\pi}{2}\right)} \)
(d) \( \tan \frac{5}{x^{2}} \)
(e) \( \sec ^{2} 3 x \)
(f) \( \cot ^{3} 5 x \)
(g) \( \frac{\sin x-\cos x}{\sin x+\cos x} \)
(h) \( 3 x^{2} \tan ^{2}(x+\pi) \)
(i) \( 3 x \cos 5 x-5 x \tan 3 x \)

5. Differentiate with respect to x :
(a) (3)/(sin (3 x+π))
(b) (5)/(tan ^2(2 x+π))
(c) (2)/(cos ^3(4 x+(π)/(2)))
(d) tan(5)/(x^2)
(e) sec ^2 3 x
(f) cot ^3 5 x
(g) (sin x-cos x)/(sin x+cos x)
(h) 3 x^2tan ^2(x+π)
(i) 3 x cos 5 x-5 x tan 3 x

Added by Jeffrey W.

Nelson Calculus and Vectors

Chris Kirkpatrick, Peter Crippin 12th Edition

Chapter 5

Instant Answer

Solved by Expert Ishana K

Step 1

- Let \( u = 3 \) and \( v = \sin(3x+\pi) \). - \(\frac{du}{dx} = 0\). - \(\frac{dv}{dx} = \cos(3x+\pi) \cdot 3\). - Substitute into the quotient rule: \[ \frac{d}{dx}\left(\frac{3}{\sin(3x+\pi)}\right) = \frac{\sin(3x+\pi) \cdot 0 - 3 \cdot \cos(3x+\pi) \cdot Show more…

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5. Differentiate with respect to \( x \) : (a) \( \frac{3}{\sin (3 x+\pi)} \) (b) \( \frac{5}{\tan ^{2}(2 x+\pi)} \) (c) \( \frac{2}{\cos ^{3}\left(4 x+\frac{\pi}{2}\right)} \) (d) \( \tan \frac{5}{x^{2}} \) (e) \( \sec ^{2} 3 x \) (f) \( \cot ^{3} 5 x \) (g) \( \frac{\sin x-\cos x}{\sin x+\cos x} \) (h) \( 3 x^{2} \tan ^{2}(x+\pi) \) (i) \( 3 x \cos 5 x-5 x \tan 3 x \)