Question

Find $d y / d x .$ $$y=10^{\left(x^{2}\right)}+\left(x^{2}\right)^{10}$$

   Find $d y / d x .$
$$y=10^{\left(x^{2}\right)}+\left(x^{2}\right)^{10}$$

Calculus

Dale Varberg, Edwin… 9th Edition

Chapter 6, Problem 27

Instant Answer

Solved by Expert Rukhmani Jain

06/16/2021

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The derivative of a sum of functions is the sum of their derivatives. So, we can find the derivative of each function separately. Show more…

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Find $d y / d x .$ $$y=10^{\left(x^{2}\right)}+\left(x^{2}\right)^{10}$$

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Key Concepts

Power Rule

The power rule is a basic rule in differentiation that simplifies finding the derivative of functions in which the variable is raised to a constant power. According to the power rule, if f(x) = x^n, then its derivative is n*x^(n-1), which is widely used for polynomial functions.

Exponential Function Differentiation

When differentiating exponential functions, particularly those with a constant base and a variable exponent, the derivative involves multiplying the original function by the natural logarithm of the base and the derivative of the exponent. This technique is essential for handling functions of the form a^(g(x)).

Differentiation

Differentiation is the process of finding the derivative of a function, which measures how a function changes as its input changes. It is a fundamental tool in calculus used to analyze functions and determine rates of change, slopes of tangents, and optimal values.

Chain Rule

The chain rule is a method for differentiating composite functions. It states that if a function is composed of two or more functions, the derivative of the composite function is the product of the derivatives of the functions taken in order, evaluated at the appropriate points.

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