The derivative of 3x is equal to 3x ln 3. Here ln 3 denotes the natural logarithm of 3, that is, ln 3 = loge 3. In this post, we will find the derivative of 3 to the power x by the first principle of derivatives. We first recall the first principle of derivatives. The … Read more
The derivative of xn is equal to nxn-1. The function xn is read as x to the power n. The derivative of x to the n is referred to as the power rule of derivatives. In this post, we will find the derivative of xn by the limit definition of derivatives and the power rule. … Read more
In this blog post, we will find the derivative of sinxlogx, that is, sinx to the power logx, by the product rule of derivatives along with logarithmic differentiation. Let us recall the product rule of derivatives: The derivative of the product function f(x)g(x) is given as follows: $\dfrac{d}{dx}(f(x)g(x))$ $=f(x) g'(x) + f'(x) g(x)$ $\cdots (\star)$. … Read more
The derivative of x3/2 is equal to $\frac{3}{2} x^{1/2}$. In this blog post, we will find the derivative of x to the power 3/2 using the first principle and power rule. To find the derivative of $x^{\frac{3}{2}}$ using the limit definition, let us first recall the first principle of derivatives. The rule says that the … Read more
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
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
The derivative of 10x is equal to 10x ln 10. Here ln denotes the logarithm with base e, called the natural logarithm. In this post, we will learn to compute the derivative of 10 raised to x. Derivative of 10x Question: What is the derivative of 10x? Answer: The derivative of 10x is 10x ln … Read more
The derivative of 2x is equal to 2x ln2. Here, ln denotes the natural logarithm (logarithm with base e). In this post, we will find the derivative of 2 to the power x. Derivative of 2x Formula As we know that the derivative of ax is axln a, the formula for the derivative of 2x … Read more
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
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