ddxtanx=sec2x,ddxsinx=cosx ddxf(x)g(x)=g(x)f′(x)−f(x)g′(x)(g(x))2 Derivative of a function is nothing but the rate of change of function. Answer and Explanation:1 (1) Givenf(x)=5+4tan(3x+1) ...
$\operatorname{arcsec} (2^x)$.More importantly, for a composite function involving three functions (say, f , g and h ), applying the Chain Rule twice yields that:\begin{align*} f(g[h(c)])’ & = f'(g[h(c)]) \, \left[ g[h(c)] \right]’ \\ & = f'(g[h(c)]) \...
Find the derivative of the following: \dfrac{d}{dx} (arcsec(x^2)). Find the derivative of the following: F(x) = ln(x^3 - 3)^4. Find the derivative of the following: G(w) = \dfrac{5}{9w^4} + 5 \sqrt 3 {w}.
Find the derivative of the following: f(\theta) = ln|sec5\theta + cot4\theta|. Find the derivative of the following: y = 5x^4 + 9x^3 +12x^2 - 7x Find the derivative of the following: \dfrac{d}{dx} (arcsec(x^2)).
Find the derivative of the following functions. (A) y=xe5x (B) s(x)=45(3x3−8)32 Derivative of the Function: You have to find the derivative of the given functions. You will use the chain rule of differentiation and standard formula of differentiation to get the...
\ f(x) = (2x - 3)^4(x^2+x+1)^5 Find the derivative of the following: h(x) = 2.1 + 0.5t - 1.1t^3. Find the derivative of the following: F(t) = 0.2t^3 - 3.1t + 13.2. Find the derivative of the following: \dfrac{d}{dx} (arcsec(x^2)). Find the derivat...
Properties of Differentiation: For a given function, f(x)=ag(x)⇒f′(x)=ag(x)ln|a|.g′(x) Also, f(x)=ln|g(x)|⇒f′(x)=1g(x).g′(x) Answer and Explanation:1 (a) {eq}\displaystyle \begin{align} f(x)&=3^{2x-1}\\Rightarrow... ...
Compute the derivative of the following function. h(x)=5x(x2+x)(6−x) Differentiation The product rule in differentiation states that ddxf(x)g(x)=f(x)g′(x)+g(x)f′(x) We need to know that ddxuv=vu′−uv′v2. This is an application of the product rule...
The derivative of the product of two functions is defined as the first function multiplied by the derivative of the second function plus the second function multiplied by the first function, according to the product rule of differentiation. ddx(f(x)⋅g(x))=f(x)g′(x)+g(x)f′(x)...
f(x+h)−f(x)h ashapproaches zero. Answer and Explanation:1 Find the derivative of the function.f(x)=ex−xx {eq}f'(x)= \frac{d}{dx}\left(e^x\right)-... Learn more about this topic: Derivatives: The Formal Definition