Take the derivative of y' to get y''. You will need the product rule and the chain rule.jendoley said:Find the first and second derivative--simplify your answer.
y=x tanx
I solved the first derivative.
y'=(x)(sec^2(x)) +(tanx)(1)
y'=xsec^2(x) +tanx
I don't know about the second derivative though.
The derivative of xtan(x) is sec^2(x) + xtan(x).
To find the derivative of xtan(x), you can use the product rule or the quotient rule. Alternatively, you can rewrite xtan(x) as x * tan(x) and use the chain rule.
The derivative of xtan(x) is important because it allows us to calculate the rate of change of a function that involves both x and tan(x). It is also used in many applications, such as optimization problems and physics equations.
Yes, the derivative of xtan(x) can be simplified using trigonometric identities. For example, sec^2(x) + xtan(x) can be rewritten as sec(x) * (tan(x) + x).
The derivative of xtan(x) can be applied in real life in various fields, such as engineering, physics, and economics. For example, it can be used to calculate the velocity of a moving object, the rate of change of a stock price, or the optimal angle for a ramp.