Using product rule,differentiate the following with respect to x:(i) y

1.	Using product rule,differentiate the following with respect to x:(i) y = (x3 + x2 + 1)sinx(ii) y = (x2 - 5x + 6)secx
Answer» (i) dy/dx = (x³ + x² + 1)d/dx sinx + sinx d/dx(x³ + x² + 1) = (x³+ x² + 1)cosx + (3x² + 2x)sinx (ii) dy/dx = (x² - 5x + 6)d/dx(secx) + sec. d/dx(x² - 5x + 6) = (x² - 5x + 6)secxtanx + secx.(2x - 5)

Using product rule,differentiate the following with respect to x:(i) y = (x3 + x2 + 1)sinx(ii) y = (x2 - 5x + 6)secx

Answer»

(i) dy/dx = (x³ + x² + 1)d/dx sinx + sinx d/dx(x³ + x² + 1)

= (x³+ x² + 1)cosx + (3x² + 2x)sinx

(ii) dy/dx = (x² - 5x + 6)d/dx(secx) + sec. d/dx(x² - 5x + 6)

= (x² - 5x + 6)secxtanx + secx.(2x - 5)

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