How do you differentiate f(x) = sec(x^2 + 1)^2f(x)=sec(x2+1)2?

2 Answers

4x (x^2 + 1) * sec(x^2 + 1)^2 * tan(X^2 + 1)^24x(x2+1)sec(x2+1)2tan(X2+1)2

Explanation:

The derivative of the sec of a function is the sec of the function multiplied by the tan of the function multiplied by the derivative of the function. And the derivative of a function to a power is, by the power rule, the power times the function raised to one less than the given power, times the derivative of the function. And the derivative of a polynomial function is the power times the coefficient times the variable raised to one less than the given power.

Sep 1, 2015

Here is the "How" using notation.

Explanation:

f(x) = sec(x^2+1)^2f(x)=sec(x2+1)2

d/dx(secu) = secutanu (du)/dxddx(secu)=secutanududx, so we get

f'(x) = sec(x^2+1)^2tan(x^2+1)^2 * d/dx((x^2+1)^2)

= sec(x^2+1)^2tan(x^2+1)^2 * 2(x^2+1)d/dx(x^2+1)

= sec(x^2+1)^2tan(x^2+1)^2 * 2(x^2+1)(2x)

= 4x(x^2+1) sec(x^2+1)^2tan(x^2+1)^2