Differentiate the following function. OA) OB) O c) OD) ƒ'(x) = ƒ'(x) = ƒ'(x) = D) f'(x) = ƒ(x) = e +tan(x) cos(x) cos(x) (e+cot²(x))+sin(x) (e*+tan(x)) cos² (x) cos(x) (eª+sec²(x))+sin(x)(eª+tan(x)) cos²(x) -sin(x) (e+tan(x))-cos(x) (e+cot²(x)) cos² (x) e+sec²(x))+sin(x) (e+tan(x)) cos(x)

given that f(x)=(e^x+tanx)/cosx f'(x)=d/dx((e^x+tanx)/cosx) by the quotient rule d/dx[f(x)/g(x)] = ([d/dxf(x)]g(x)-f(x)[d/dxg(x)])/[g(x)]^2

Resuelto Differentiate the following function. OA) OB) O c)

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Pregunta: Differentiate the following function. OA) OB) O c) OD) ƒ'(x) = ƒ'(x) = ƒ'(x) = D) f'(x) = ƒ(x) = e +tan(x) cos(x) cos(x) (e+cot²(x))+sin(x) (e*+tan(x)) cos² (x) cos(x) (eª+sec²(x))+sin(x)(eª+tan(x)) cos²(x) -sin(x) (e+tan(x))-cos(x) (e+cot²(x)) cos² (x) e+sec²(x))+sin(x) (e+tan(x)) cos(x)
Differentiate the following function. OA) OB) O c) OD) ƒ'(x) = ƒ'(x) = ƒ'(x) = D) f'(x) = ƒ(x) = e +tan(x) cos(x) cos(x) (e+cot²(x))+sin(x) (e*+tan(x)) cos² (x) cos(x) (eª+sec²(x))+sin(x)(eª+tan(x)) cos²(x) -sin(x) (e+tan(x))-cos(x) (e+cot²(x)) cos² (x) e+sec²(x))+sin(x) (e+tan(x)) cos(x)

Muestra el texto de la transcripción de la imagen
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Solución
Paso 1
given that $f (x) = \frac{e^{x} + \tan x}{\cos x}$
$f^{'} (x) = \frac{d}{d x} (\frac{e^{x} + \tan x}{\cos x})$
by the quotient rule $\frac{d}{d x} [\frac{f (x)}{g (x)}] = \frac{[\frac{d}{d x} f (x)] g (x) - f (x) [\frac{d}{d x} g (x)]}{{[g (x)]}^{2}}$
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Texto de la transcripción de la imagen:

Differentiate the following function.

f (x) = \frac{e ^{x} + t a n ( x )}{c o s ( x )}

f^{'} (x) = \frac{c o s ( x ) ( e ^{x} + c o t ^{2} ( x ) ) + s i n ( x ) ( e ^{x} + t a n ( x ) )}{c o s ^{2} ( x )}

f^{'} (x) = \frac{c o s ( x ) ( e ^{x} + s e c ^{2} ( x ) ) + s i n ( x ) ( e ^{x} + t a n ( x ) )}{c o s ^{2} ( x )}

f^{'} (x) = \frac{- s i n ( x ) ( e ^{x} + t a n ( x ) ) - c o s ( x ) ( e ^{x} + c o t ^{2} ( x ) )}{c o s ^{2} ( x )}

f^{'} (x) = \frac{( e ^{x} + s e c ^{2} ( x ) ) + s i n ( x ) ( e ^{x} + t a n ( x ) )}{c o s ( x )}

f^{'} (x) = \frac{c o s ( x ) ( e ^{x} + c o t ^{2} ( x ) ) + s i n ( x ) ( e ^{x} + t a n ( x ) )}{c o s ^{2} ( x )} f^{'} (x) = \frac{c o s ( x ) ( e ^{x} + s e c ^{2} ( x ) ) + s i n ( x ) ( e ^{x} + t a n ( x ) )}{c o s ^{2} ( x )} f^{'} (x) = \frac{- s i n ( x ) ( e ^{x} + t a n ( x ) ) - c o s ( x ) ( e ^{x} + c o t ^{2} ( x ) )}{c o s ^{2} ( x )} f^{'} (x) = \frac{( e ^{x} + s e c ^{2} ( x ) ) + s i n ( x ) ( e ^{x} + t a n ( x ) )}{c o s ( x )} f^{'} (x) = \frac{( e ^{x} + c o t ^{2} ( x ) ) - s i n ( x ) ( e ^{x} + t a n ( x ) )}{c o s ( x )}