1. Determine the derivatives of the following functions: (i) f(x) = csc(x) (ii) g(x) = √2x cos(x) tan (3x) sin(x) (iv) k(x) = cos(x²) + cos² (x) (v) m(x) = (x³ + tanª (vi) p(x) = ecos² (-x) (vii) 2(2) = In (cos(x)}) (viii) w(x) = 7(2 cos (3x) sin(3x)) (ix) y(x) = log₁(√x³ - e²x)¹1 (iii) h(x) = X 12 3

1. f(x)=cosec(x)=1/(sin(x) Using the quotient rule, we have

Resuelto 1. Determine the derivatives of the following

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Pregunta: 1. Determine the derivatives of the following functions: (i) f(x) = csc(x) (ii) g(x) = √2x cos(x) tan (3x) sin(x) (iv) k(x) = cos(x²) + cos² (x) (v) m(x) = (x³ + tanª (vi) p(x) = ecos² (-x) (vii) 2(2) = In (cos(x)}) (viii) w(x) = 7(2 cos (3x) sin(3x)) (ix) y(x) = log₁(√x³ - e²x)¹1 (iii) h(x) = X 12 3
1. Determine the derivatives of the following functions: (i) f(x) = csc(x) (ii) g(x) = √2x cos(x) tan (3x) sin(x) (iv) k(x) = cos(x²) + cos² (x) (v) m(x) = (x³ + tanª (vi) p(x) = ecos² (-x) (vii) 2(2) = In (cos(x)}) (viii) w(x) = 7(2 cos (3x) sin(3x)) (ix) y(x) = log₁(√x³ - e²x)¹1 (iii) h(x) = X 12 3

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Solución
Paso 1
1. $f (x) = \cos e c (x) = \frac{1}{\sin (x)}$

Using the quotient rule, we have
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Texto de la transcripción de la imagen:

1. Determine the derivatives of the following functions: (i)

f (x) = csc (x)

(ii)

g (x) = 2 x cos (π x)

(iii)

h (x) = \frac{t a n ( 3 x )}{s i n ( x )}

(iv)

k (x) = cos (x^{2}) + cos^{2} (x)

(v)

m (x) = (x^{3} + tan^{4} (\frac{x}{12}))^{3}

(vi)

p (x) = e^{c o s^{2} (- x)}

(vii)

q (x) = ln (\frac{c o s ( x )}{x ^{- 1} - 5})

(viii)

w (x) = 7^{(2 c o s (3 x) s i n (3 x))}

(ix)

y (x) = lo g_{4} (x^{3} - e^{2 x})^{11}