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The derivative of x^sinx (x to the power sinx) is equal to xsinx[sinx/x + cosx logx]. Here we learn how to differentiate x^sinx. Derivative of xsinx Formula xsinx Derivative Formula: The formula of xsinx derivative is given by d/dx(xsinx) = xsinx[sinx/x + cosx logx] Let us now give a proof of this fact. Derivative of … Read more

The derivative of 1/(cube root of x) is equal to $-\dfrac{1}{3\sqrt[3]{x^4}}$. Note that 1/(cube root of x) can be written mathematically as $\frac{1}{\sqrt[3]{x}}$. In this post, we will learn how to differentiate 1/(cube root of x). Derivative of 1/cube root x by Power Rule To find the derivative of 1/cube root of x, we will … Read more

The derivative of x^4 is equal to 4×3 which can by proved by first principle and power rule. The formula of the derivative of x4 is given below. $\dfrac{d}{dx}$(x4) = 4×3. Let us now learn how to differentiate x to the power 4 by the power rule and the first principle of derivatives. Derivative of … Read more

The derivative of a^x (a to the power x) is equal to axlna where ln denotes the natural logarithm, that is, lna=logea. In this post, we will learn how to differentiate a^x using the limit definition. The derivative formula of a^x is the following. $\dfrac{d}{dx}(a^x)=a^x\ln a$. The first principle or the limit definition of derivatives … Read more

The derivative of 1/(1+x) is equal to -1/(1+x)2. In this post, we will find the derivative of 1 divided by 1+x using the limit definition, that is, by the first principle. The first principle of derivatives says that the derivative of a function f(x) is given by the following limit: $\dfrac{d}{dx}(f(x))$ $=\lim\limits_{h \to 0} \dfrac{f(x+h)-f(x)}{h}$ … Read more

The derivative of square root of logx is equal to 1/(2x root(logx)). In this post, we will learn how to differentiate root logx by the chain rule of derivatives. The formula for the derivative of root logx is given below. $\dfrac{d}{dx}(\sqrt{\log x})$ $=\dfrac{1}{2x\sqrt{\log x}}$ Derivative of Root logx by Chain Rule By chain rule of … Read more

The derivative of 1/(1+x) is equal to -1/(1+x)2. The function 1/(1+x) is the reciprocal of 1+x. In this post, we will learn how to differentiate 1 divided by 1+x. Its derivative is denoted by $\dfrac{d}{dx} \Big(\dfrac{1}{1+x} \Big)$ and it is equal to $\dfrac{d}{dx} \Big(\dfrac{1}{1+x} \Big)$ $=\dfrac{-1}{(1+x)^2}$. We will use the chain rule and the quotient … Read more

The Derivative of (ax+b)/(cx+d) is equal to (ad-bc)/(cx+d)2. In this post, we will learn how to differentiate the quotient function (ax+b)/(cx+d). The derivative of (ax+b)/(cx+d) is denoted by the symbol $\dfrac{d}{dx}\left( \dfrac{ax+b}{cx+d}\right)$ and it is equal to $\dfrac{d}{dx}\left( \dfrac{ax+b}{cx+d}\right)$ $=\dfrac{ad-bc}{(cx+d)^2}$ when the denominator cx+d is nonzero, that is, x ≠ -d/c. How to Differentiate (ax+b)/(cx+d) … Read more

Derivative of absolute value of x. The derivative of mod x is denoted by d/dx(|x|) and it is equal to x/|x| for all nonzero values of x. In this post, we will learn how to differentiate modulus x. Recall that mod x is defined as below. $|x|=\begin{cases} x, & \text{ if } x\geq 0 \\ … Read more