The derivative of cosx/x (cosx divided by x) is equal to -(xsinx +cosx)/x2. Here we will learn to differentiate cosx/x by the quotient rule as well as implicit differentiation method. Let us now differentiate cosx/x. Derivative of cosx/x by Quotient Rule By the quotient rule, the derivative of $\dfrac{f}{g}$ is given by $\dfrac{d}{dx}\big( \dfrac{f}{g}\big)=\dfrac{gf’ -fg’}{g^2}$ … Read more
The derivative of x^1/x (x to the power 1/x) is denoted by d/dx(x1/x) and its value is equal to x1/x[1/x2 – 1/x2 ⋅ logex]. The derivative formula of x1/x is given below: d/dx(x1/x) = x1/x -2 [1 – logex]. Let us now learn how to differentiate x1/x. Derivative of x to the power 1/x Question: … Read more
The derivative of x^tanx (x to the power tanx) is denoted by d/dx(xtanx) and its value is equal to xtanx[tanx/x + sec2x logex]. The derivative formula of xtanx is given by d/dx(xtanx) = xtanx[tanx/x + sec2x logex]. Let us now learn how to differentiate xtanx. Differentiate xtanx Question: Prove that d/dx(xtanx) = xtanx[tanx/x + sec2x … Read more
The derivative of x^π (x to the power pi) is equal to πxπ-1. In this post, we will learn how to differentiate x to the power pi with respect to x. The derivative of xπ is denoted by d/dx (xπ) or (xπ)’. Its formula is given by $\dfrac{d}{dx}(x^\pi)=\pi x^{\pi -1}$. Derivative of x to the … Read more
The derivative of x^e (x to the power e) is equal to exe-1. Here we will learn to differentiate x^e with respect to x. The derivative of xe is denoted by d/dx (xe) or (xe)’. Its formula is given by $\dfrac{d}{dx}(x^e)=ex^{e-1}$. Derivative of x to the power e Question: Find the derivative of xe, that … Read more
The derivative of x^cosx (x to the power cosx) is equal to xcosx[cosx/x – sinx logex]. Here we learn how to differentiate x^cosx. The derivative of xcosx is denoted by d/dx(xcosx) and its formula is given below: d/dx(xcosx) = xcosx[cosx/x – sinx logex]. Let us now give a proof of xcosx derivative. Differentiate xcosx Question: … Read more
The derivative of root tanx is equal to -cosec2x/(2√cotx). Here we will differentiate square root of cot x by chain rule and also using the first principle of derivatives. The derivative formula of root cotx is given by $\dfrac{d}{dx}(\sqrt{\cot x})=-\dfrac{\text{cosec}^2 x}{2\sqrt{\cot x}}$. Derivative of square root of cotx from first principle Question: Find the derivative … Read more
The derivative of x^6 (x to the power 6) is equal to 6×5. Here, we will find the derivative of x6 using the power rule and the first principle of derivatives. The derivative of x6 is denoted by d/dx (x6). The derivative formula of x6 is as follows: $\dfrac{d}{dx}(x^6)=6x^5$. Derivative of x^6 by Power Rule … Read more
The derivative of x^10 (x to the power 10) is 10×9. In this post, we will find the derivative of x10 by the first principle and the power rule of derivatives. The derivative of x10 is denoted by d/dx (x10), and its formula is given by $\dfrac{d}{dx}(x^{10})=10x^9$. Derivative of x^10 by First Principle The derivative … Read more
The derivative of root secx is equal to (secx tanx)/(2√secx). In this post, we will learn how to find the derivative of root secx by first principles. The formula of the derivative of square root of secx is given as follows: $\dfrac{d}{dx}(\sqrt{\sec x})=\dfrac{\sec x\tan x}{2\sqrt{\sec x}}$. Derivative of square root of secx from first principle … Read more