Derivative

Derivative of (ax+b)/(cx+d) | (ax+b)/(cx+d) Derivative

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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 mod x | Mod x Derivative

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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

Derivative of x^x [x to the power x] | d/dx(x^x)

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The derivative of xx is equal to xx(1+ln x). That is, d/dx(xx)=xx(1+ln x). This can be proved by the logarithmic differentiation. Here, ln=loge. In this post, we will learn how to find the derivative of x to the x. Derivative of xx Formula The formula of xx derivative is given by d/dx(xx)=xx(1+ln x) Derivative of … Read more

Derivative of cos2x by First Principle, Chain Rule

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The derivative of cos2x is equal to -2sin2x.  In this post, we will find the derivative of cos2x by the first principle, that is, by the limit definition of derivatives as well as by the chain rule of derivatives. Recall the first principle of derivatives. By this rule, we know that the derivative of a … Read more

Derivative of 3^x by First Principle

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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

Derivative of x^n by First Principle, Power Rule

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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

What is the Derivative of (sinx)^logx

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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

Derivative of x^3/2: by First Principle, Power Rule

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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

Derivative of 2^x by First Principle

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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