y = \cos^{-1}(x^2) Find the derivative of s(t) = (1 + e^t) ln t. Find the derivative of y a) y = x In x / 1+ In x Find the derivative of \frac{(x^{2} + 9)}{(x - 3)}. Find the derivative. f(x)= \frac{\sin(2x^2)}{\cos(2x+2)} Find the derivative...
sin(x2) is made up of sin() and x2: f(g) = sin(g) g(x) = x2 The Chain Rule says: the derivative of f(g(x)) = f'(g(x))g'(x) The individual derivatives are: f'(g) = cos(g) g'(x) = 2x So: d dx sin(x2) = cos(g(x)) (2x) = 2x cos(x2)Another...
i)(cosx)′=−sinxii)(tanx)′=sec2xiii)(tanu)′=sec2uu′ with u a function of xAnswer and Explanation: We have a function composed of the tangent function whose argument is the trigonometric function cosine. We must apply the rule for the derivative of......
The derivative off(x)=x2+2xatx=2is View Solution The derivative off(x)=2√x−1xis View Solution The anti - derivative off(x)=ex/2whose graph passes through the point (0,3) is : View Solution Free Ncert Solutions English Medium ...
Find the derivative of f(x)=2x+1x+3 View Solution The derivative of f(x)=x+22x+1 is View Solution The derivative of f(x)=2√x−1xis View Solution The derivative of f(x)=sin2x is View Solution The derivative of f(x)=x−3(3+7.x) is View Solution ...
derivative of sin6(x) Solution 6sin5(x)cos(x)Hide Steps Solution steps dxd(sin6(x)) Apply the chain rule:6(sin(x))5dxd(sin(x)) =6(sin(x))5dxd(sin(x)) dxd(sin(x))=cos(x) =6(sin(x))5cos(x) Simplify=6sin5(x)cos(x)...
limit as x approaches infinity of x^{2x}x→∞lim(x2x)derivative of cos(2x+sin(2pi))dxd(cos(2x)+sin(2π))integral from 1 to t of (25)/(x^3)∫1tx325dxderivative of cos(x+a)dxd(cos(x+a))inverse oflaplace 7/(s^5)inverse laplaces57 ...
The derivative of a function f(x) tells the rate of change of f(x) with respect to x. {eq}\frac{d}{dx} \sin ax =a \cos x \\ \frac{d}{dx} \cos ax =-a \sin x \\ {/eq} Differentiation:Definition using Limits: We define the derivative of a function as {eq}\dfrac{dy}...
Find the derivative of y = 2cot^(-1)(sqrt(2x)) - sin^(-1)(2x + 1). Find the derivative of the function.f(x)=\ln \left ( \frac{x(x-1)}{x-2} \right ) Find the given derivative Dx \left [ 2x^{-\frac{1}{3 + \frac{9}{x^{\frac{5}{3} \right ] Find...
d/dx cos(x) = - sin(x) d/dx tan(x) = 1 - tan2(x) d/dx arcsin(x) = 1/sqrt(1-x2) d/dx arccos(x) = -1/sqrt(1-x2) d/dx arctan(x) = 1/(1+x2) Applications of the Derivative The derivative comes up in a lot of mathematical problems. An example is finding the ...