1 Power x a a x a-1 Exponential e x e x Exponential a x a x ln a Natural logarithm ln(x) Logarithm logb(x) Sine sin x cos x Cosine cos x -sin x Tangent tan x Arcsine arcsin x Arccosine arccos x Arctangent arctan x Hyperbolic sine sinh x cosh x Hyperbolic cosine cosh x ...
Find the following derivative. y = 2xsinh^{-1}(2x) - \sqrt{1 + 4x^2} Find the following derivative. f(t) = sech^{-1}(2x) Find the following derivative. d/{dx} [(x + 1)^{3 x}] Find the following derivative. (x^5 + 4) \ln x ...
What is the derivative of (\ln(x))^x ? What is the derivative of \frac{-1}{(x-1)^2}? What is the derivative of ln(x+9)? What is the derivative of y = (e^(-x^2))(ln(tan x))? What is the derivative of ln(sinh x)?
+x^(100), then find f'(1). 02:48 Find the derivative of (sqrt(x) - 3x) (x + 1/x) Text Solution Find the derivative of 5 sin x + e^(x) log x . 01:48 Find the derivative of 5^(x) + log x + x^(2) e^(x) 01:35 Find the derivative of y = e^(2x)log (3x ...
The derivative of f(x)=log(cosh(x)-1) is sinh(x)cosh(x)−1 as you wrote, and that is not among the given answers.May 3, 2017 #7 Mark44 Mentor Insights Author 37,791 10,183 Ryansf98 said: f'(x) = [1/cosh(x) - 1] * d/dx [cosh(x) - 1], => f'(x...
•ln(x)—natural logarithm •sin(x)—sine •cos(x)—cosine •tan(x)—tangent •cot(x)—cotangent •arcsin(x)—arcsine •arccos(x)—arccosine •arctan(x)—arctangent •arccot(x)—arccotangent •sinh(x)—hyperbolic sine ...
Find the following derivative. y = 2xsinh^{-1}(2x) - \sqrt{1 + 4x^2} Find the following derivative. d/dx ((19 + 6x^2)^7 e^9 - 2x) Find the following derivative. h(x) = x^2coth^{-1}x Find the derivative of f (x) = x^3 - 4 x^2 + x at -2. That is, find ...
Derivativef′of the functionf(x)=sinxis:∀x∈]−∞,+∞[,f′(x)=cosx Proof/Demonstration sin(x+h)−sinxh=sin(x)cos(h)+cos(x)sin(h)−sinxhsin(x+h)−sinxh=sinhh×cosx+sinx×coshh−sinx×1hsin(x+h)...
Derivative f’ of function f(x)=arcsin x is: f’(x) = 1 / √(1 - x²) for all x in ]-1,1[. To show this result, we use derivative of the inverse function sin x. Derivative of arcsin x f′ f(x)=arcsinx ∀x∈]–1,1[,f′(x)=11−x2 ...
What is the derivative ofsec−1(x+2)2=2(x+2)(x+2)−1? Differentiation of sec−1x=1xx2−1 Answer and Explanation:1 Lety=sec−1(x+2)2 Differentiation wrt x: {eq}\frac{dy}{dx}=\frac{1}{(x+2)^2\sqrt{(x+2)^4-1}} . \frac{d}{d...