Differentiate the function \( g(x)=5 x^{2}+7 \tan x \)

To differentiate the function \( g(x) = 5x^2 + 7\tan x \), we apply the power rule and the derivative of the tangent function. The derivative of \( 5x^2 \) is \( 10x \), and the derivative of \( 7\tan x \) is \( 7\sec^2 x \). Therefore, the derivative \( g'(x) \) is: \[ g'(x) = 10x + 7\sec^2 x \] Isn’t it fascinating how calculus combines different rules to make sense of change? You’re not just working with numbers; you’re uncovering the behavior of functions all around us—ripples in a pond, the shape of a rollercoaster, or even the stock market trends! As you explore more about differentiation, remember the chain rule and product rule! They’re your trusty companions when tackling more complex functions, ensuring that you never miss a beat in understanding how derivatives interact with functions, especially when you start mixing polynomials, trigonometric, and exponential terms!