Derivative

Derivative of 2^x by First Principle

by

The derivative of 2x is equal to 2xln2 where ln 2 is the natural logarithm of 2, that is, ln 2 = loge2. In this post, we will find the derivative of 2x by the first principle of derivatives. Derivative of 2x from First Principle We know that the derivative of a function f(x) by … Read more

Derivative of xe^x by First Principle, Product Rule

by

The derivative of xex is equal to (1+x)ex. In this post, we will find the derivative of xex by the first principle and by the product rule of derivatives. The first principle of derivatives says that the derivative of a function f(x) is given by the following limit formula:   $\dfrac{d}{dx}(f(x))$ $=\lim\limits_{h \to 0} \dfrac{f(x+h)-f(x)}{h}$ … Read more

Find the Derivative of sin5x [by First Principle]

by

The derivative of sin5x is equal to 5cos5x.  In this post, we will find the derivative of sin5x by the first principle, that is, by the limit definition of derivatives. By the first principle of derivatives, we know that the derivative of a function f(x) is given by the following limit: $\dfrac{d}{dx}(f(x))$$=\lim\limits_{h\to 0} \dfrac{f(x+h)-f(x)}{h}$ …(I) Derivative … Read more

Derivative of cos(e^x) by Chain Rule

by

The derivative of cos(ex) is equal to -ex sin(ex). In this post, we will learn how to find the derivative of cos(ex) by the chain rule of derivatives. Derivative of cos(ex) Question: Find the derivative of cos(ex). Answer: The derivative of cos(ex) is equal to -exsin(ex). Explanation: Note that f(x)=cos(ex) is a composite function. The … Read more

[Solved] What is the Derivative of e^1/x?

by

The derivative of e1/x is $-\frac{1}{x^2} e^{1/x}$. So if y=e1/x, then dy/dx = -1/x2 e1/x. In this post, we will learn how to differentiate e to the power 1/x. Derivative of e1/x Question: What is the derivative of e raised to 1/x? Answer: The derivative of e raised to 1/x is equal to $-1/x^2 e^{1/x}$. … Read more