The derivative of root 1-x^2 is equal to -x/√(1-x2). Here we differentiate square root of 1-x2 by chain rule and implicit differentiation method. Note that $\dfrac{d}{dx} \Big( \sqrt{1-x^2}\Big)=-\dfrac{x}{\sqrt{1-x^2}}$. Let us now differentiate root 1-x2. Derivative of root 1-x2 by Chain Rule Question: Find the derivative of square root 1-x2. Answer: Let us put z = … Read more
The derivative of sec2x by first principle is equal to 2sec2x tan2x. In this post, we will find the derivative of sec2x by first principle. The first principle rule of derivatives states that the derivative of f(x) is given by the limit f$’$(x) = limh→0 $\dfrac{f(x+h)-f(x)}{h}$. Let us now find the differentiation of sec2x by … Read more
The derivative of x^logx (x to the power logx) is equal to 2 logx xlogx-1. Here we find the differentiation of xlogx by using the product rule of derivatives together with logarithmic differentiation. The product rule of derivatives states the following: $\dfrac{d}{dx}$(f(x)g(x)) = f(x) $\dfrac{d}{dx}$(g(x)) + g(x) $\dfrac{d}{dx}$(f(x)) …(I) Find the Derivative of xlogx Answer: … Read more
The derivative of cos cube x (cos^3x) is equal to -3cos2x sinx. In this post, we will find the derivative of cos cube x using the chain rule. The derivative formula of cos3x is given as follows: d/dx (cos3x) = -3cos2x sinx. Derivative of Cos^3x The derivative of cos3x is -3cos2x sinx. Explanation: As cos3x … Read more
The derivative of sinx/x is equal to (xcosx -sinx)/x2. Here we will learn how to differentiate sinx/x with respect to x. The derivative formula of sinx/x is given by $\dfrac{d}{dx}(\dfrac{\sin x}{x})$ = $\dfrac{x\cos x -\sin x}{x^2}$. Find the Derivative of sinx/x As sinx/x is a quotient function, to find the derivative of sinx/x we will … Read more
The derivative of coshx, denoted by d/dx(coshx), is equal to sinhx. Here we will learn how to differentiate cosh(x), i.e, how to find the derivative of the hyperbolic cosine function with respect to x. The formula of the derivative of coshx is given below: d/dx[coshx] = sinhx. To find the differentiation of coshx, we will … Read more
The derivative of sinhx, denoted by d/dx(sinhx), is equal to coshx. In this post, we will learn how to differentiate sinh(x), i.e, how to find the derivative of the hyperbolic sine function with respect to x. The derivative formula of sinhx is given as follows: d/dx[sinhx] = coshx. Before differentiating sinh(x), let us first recall … Read more
The derivative of tanh(x), denoted by d/dx tanh(x), is equal to sech2x. In this post, we will learn how to differentiate tanh(x), i.e, how to find the derivative of the hyperbolic tan function with respect to x. The derivative formula of tanh(x) is given as follows: d/dx[tanh(x)] = sech2x. How to Differentiate tanh(x) As tanh … Read more
The derivative of cot^2x is -2cotx cosec2x. Here we find the derivative of cot square x by the first principle of derivatives. Differentiation of cot square x by the first principle will be computed as follows. Derivative of cot square x by First Principle By first principle, the derivative of f(x) is given by the … Read more
The derivative of tan^2x is 2tanx sec2x. Here we will find the derivative of tan square x by the first principle of derivatives. The first principle says that the derivative of a function f(x) is given by the following limit formula: $\dfrac{d}{dx}(f(x))$ = limh→0 $\dfrac{f(x+h)-f(x)}{h}$ …(I) Let us now learn how to differentiate tan square … Read more