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This calculus math tutorial from NutshellMath offers homework help in finding the derivatives of compound functions using the chain rule. The chain rule states that if f and g are both differentiable functions, and if F is a composite function of f and g, such that F(x)=f(g(x)), that F is differentiable, and F’ is given by the product F’(x)=f’(g(x))*g’(x). In practical terms, the chain rule states that the derivative of a composite function of two differentiable functions will be equal to derivative of the “outer” function, without altering the “inner” function, times the derivative of the “inner” function.
The chain rule can be used to find the derivative of composite functions. A common example of such a function would be a polynomial expression as a single quantity all raised to a power. In such an example, the power rule would be used first to find the derivative outside the quantity. The result would then be multiplied by the derivative of the polynomial within the parentheses.
The chain rule can also be used consecutively, to find nested functions, such as f(g(h(x))). Mastering the use of the chain rule is essential to learning how to find derivatives of more complex functions in calculus. The examples in this tutorial demonstrate how to effectively use the chain rule to find the derivative of composite functions.
This calculus math tutorial from NutshellMath offers homework help in finding the derivatives of compound functions using the chain rule. The chain rule states that if f and g are both differentiable functions, and if F is a composite function of f and g, such that F(x)=f(g(x)), that F is differentiable, and F’ is given by the product F’(x)=f’(g(x))*g’(x). In practical terms, the chain rule states that the derivative of a composite function of two differentiable functions will be equal to derivative of the “outer” function, without altering the “inner” function, times the derivative of the “inner” function.
The chain rule can be used to find the derivative of composite functions. A common example of such a function would be a polynomial expression as a single quantity all raised to a power. In such an example, the power rule would be used first to find the derivative outside the quantity. The result would then be multiplied by the derivative of the polynomial within the parentheses.
The chain rule can also be used consecutively, to find nested functions, such as f(g(h(x))). Mastering the use of the chain rule is essential to learning how to find derivatives of more complex functions in calculus. The examples in this tutorial demonstrate how to effectively use the chain rule to find the derivative of composite functions.