Find the derivative of x sec x + 1/x.

Question

Walk me through this, please

Answer 1

derivative of secx = secxtanx

derivative of xsecx = xsecxtanx + secx

(derivative of a product is 1st term times derivative of 2nd term plus the 2nd term times derivative of the 1st term)

1/x = x^-1

derivative = -x^-2 = - 1/x^2

make the exponent into the coefficient, and reduce the exponent by 1

derivative of secx + 1/x

= xsecxtanx + secx - 1/x^2

Answer 2

x sec x + 1/x

d/dx (x secx) + d/dx (1/x)

Use product rule to find d/dx (x sec x)

= x secx tanx + sec x

Use the power rule to find d/dx (1/x)

= -1/x²

xsecx tanx + sec x - 1/x²