promath The derivative of sinx/(1+cosx) [sinx divided by 1+cosx] is equal to 1/(1+cosx), and it is denoted by d/dx (sinx/1+cosx). That is, $\dfrac{d}{dx} \big(\dfrac{\sin x}{1+\cos x} \big)=\dfrac{1}{1+\cos x}$. Here we will learn how to differentiate sinx divided by 1+cosx. Differentiate sinx/(1+cosx) Question: If y= sinx/1+cosx, then find dy/dx. Answer: If y=sinx/(1+cosx), then dy/dx = 1/(1+cosx). Explanation: … Read more
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 integral of sin^5x is equal to ∫sin5x dx = -(cos5x)/5 + (2cos3x)/3 -cos x+C, where C denotes an integration constant. Here we will learn how to integrate sin^5x. The integration formula of sin5x is given by $\int \sin^5x$ $=-\dfrac{\cos^5x}{5}+\dfrac{2}{3} \cos^3x -\cos x +C$ where C is a constant. Integration of sin5x Question: Find the … Read more
Sin minus theta is equal to minus sin theta, that is, sin(-θ) = -sinθ. Here we will learn how to find the value of sin of minus theta. The sin minus x formula is given by sin(-x) = -sinx. Prove that sin(-theta) = -sin theta To compute sin(-theta), let us follow the below steps. The … Read more
Cos minus theta is equal to cos theta, that is, cos(-θ) = cosθ. Similarly, cos(-x) = cosx. In this post, we learn to find the value of cos of minus theta. The cos minus theta formula is given as follows: cos(-θ) = cosθ. Prove that cos(-theta) = cos theta We will follow the below steps … Read more
The sin(90-theta) formula is given by sin(90-θ) = cosθ. As 90°=π/2, sin(90-θ) formula can be written as follows: sin(π/2-θ) = cosθ. On the other hand, sin(θ-90) formula is given by sin(θ-90) = -cosθ. Let us now simplify the expression sin(90-theta). Simplify Sin(90-theta) Question: Simplify the expression sin(90-θ). Answer: To simplify the expression sin(90-θ), we will … 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