1) Calculate the derivatives of following functions with respect to x. (i) (ii) (iii) (iv) y...

 

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1) Calculate the derivatives of following functions with respect to x. (i) (ii) (iii) (iv) y = f (x) = x³ + (1+x²) y = (x³ + 2)² + (1 + x²) 3 y = (x³ + 2) (3x + x 0.2) y = (x0.5 + 5)²+(2x + 1) 0.5 2) Calculate the partial derivatives of following functions with respect to X₁ and with respect to X2. (i) y = f(x1,x2) = 3x₁ + 5x2 (ii) y = ƒ (x1, x2) = x² + (2x₁ + 1)³ + 4x³.x² + x₁.x². (iii) y = f(x1,x2) = x0.75x2. 0.25 (iv) y = f (x1, x2) = (x0.5x2.5) 2 (v) y = f (x1,x2) = 4x0.5 + x2 (vi) y = f(x1,x2) = x₁x2 + x² + x³ 1) Calculate the derivatives of following functions with respect to x. (i) (ii) (iii) (iv) y = f (x) = x³ + (1+x²) y = (x³ + 2)² + (1 + x²) 3 y = (x³ + 2) (3x + x 0.2) y = (x0.5 + 5)²+(2x + 1) 0.5 2) Calculate the partial derivatives of following functions with respect to X₁ and with respect to X2. (i) y = f(x1,x2) = 3x₁ + 5x2 (ii) y = ƒ (x1, x2) = x² + (2x₁ + 1)³ + 4x³.x² + x₁.x². (iii) y = f(x1,x2) = x0.75x2. 0.25 (iv) y = f (x1, x2) = (x0.5x2.5) 2 (v) y = f (x1,x2) = 4x0.5 + x2 (vi) y = f(x1,x2) = x₁x2 + x² + x³