Sine Cosine Tangent Sine Cosine Tangent Trigonometry is a mathematical branch where, we study about triangle and their relationships with sides and angle. In trigonometry, we define functions with respect to triangle and some main functions of trigonometry are sine cosine tangent.· sin x = opposite hypotenuse · cos x = adjacent hypotenuse · tan x = opposite adjacent Now, we discuss derivatives of sine cosine tangent: 1. Derivative of sine: derivative of sin x is cos x. D (sin x) = cos x Dx 2. Derivative of cosine: derivative of cos x is –sin x D (cos x) = -sin x Dx 3. Derivative of tangent: derivative of tan x is sec2 x. D (tan x) = sec2 x Dx If, u = f(x) is a function of x, Know More About Add -1/2 and 2/3
then we define derivation of sine cosine and tangent by chain rule: a) Derivative of sin u: Derivative of sin u is multiplication of cos u and Du/Dx D (sin u) = cos u . Du Dx Dx b) Derivative of cos u: Derivative of cos u is multiplication of –sin u and Du/Dx D (cos u) = -sin u . Du Dx Dx c) Derivative of tan u : derivative of tan u is multiplication of sec2 u and Du/Dx (tan u) = sec2 u . Du Dx x Now, we take different examples to understand derivatives of sine cosine tangent: 1. Find derivative of y where y = sin(x2 + 3) y = D (sin (x2 + 3)) = cos (x2 + 3) . D (x2 + 3) = cos (x2 + 3) . (2x) Dx Dx Dx 2. Find derivative of y where y = cos 3x4 Dy = D (cos 3x4) = -sin 3x4 . D (3x4) = -sin 3x4 . 3(4x3) = 12x3.sin 3x4 x Dx x 3. Find derivative of y where y = x.tan x Dy = D (x.tan x) = x . D (tan x) + tan x . D (x) = x.sec2 x + tan x Dx Dx Dx DX
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