Find an equation of the tangent line to the given curve at the given point. y=√(1+2 x^2) at x=

step 1 We are given the equation y is equal to the root of 1 plus 2x squared. And we are to find the eq

Find an equation of the tangent line to the given curve at...

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Key Concepts

Tangent Line

The tangent line to a curve at a given point is the line that just touches the curve at that point and has the same instantaneous slope as the curve. It represents the best linear approximation of the function at that point, and its equation is typically determined using the point of tangency and the derivative of the function, which provides the slope.

Derivative

The derivative of a function measures the rate at which the function’s value changes with respect to changes in the input value. It gives the slope of the tangent line at any point on the function. In problems involving tangent lines, computing the derivative at the point of interest yields the slope needed to formulate the equation of that line.

Chain Rule

The chain rule is a fundamental rule in calculus used to differentiate composite functions, where one function is applied inside another. In cases where the function involves an outer function, like a square root, and an inner function, such as a quadratic expression, the chain rule is used to differentiate the composite expression by multiplying the derivative of the outer function by the derivative of the inner function.

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