116K Understand what derivative calculus is and how to find the derivative of a function. Learn the derivative rules, and practice taking derivatives by following examples. Related to this QuestionWhat is the derivative of this? h(x) = sin (e^3x) What is the derivative of 2x \sin x(3x...
Find the derivative of the function. y=\int_{\cos x}^{\sin x} \ln(9+5v)dv Find the derivative: f(x) = \frac{\sqrt{x{3x + 1} Find the derivative of y=\sec^{-1}(\sqrt x) Find the derivative of \left ( \frac{2x}{1 + x} \right )^{e^{x. ...
ddxsin(x) = cos(x) Or: sin(x)’ = cos(x)Power RuleExample: What is ddxx3 ? The question is asking "what is the derivative of x3 ?" We can use the Power Rule, where n=3: ddxxn = nxn−1 ddxx3 = 3x3−1 = 3x2 (In other words the derivative of x3 is 3x2)So...
Frequently Asked Questions (FAQ) What is the derivative of sin^6(x) ? The derivative of sin^6(x) is 6sin^5(x)cos(x) What is the first derivative of sin^6(x) ? The first derivative of sin^6(x) is 6sin^5(x)cos(x)Study...
dxd(3x−y)=3 dxdx=1 =x23x−1⋅(3x−y) Simplify=x2y Enter your problem Popular Examples (\partial)/(\partial x)(x^{0.2}y^{0.4})∂x∂(x0.2y0.4)limit as x approaches 3 of (3-x)/(x^2-9)x→3lim(x2−93−x)integral of 1/(sqrt(x^2...
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}...
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Find the second derivative of sin 3x cos 5x. 07:14 If y=e^tanx then prove that: cos^2x(d^2y)/(dx^2)-(1+sin2x)(dy)/dx=0 03:59 If y=(logx)/x , show that (d^2y)/(dx^2)=(2logx-3)/(x^3) . 01:39 If y=e^(ax)cosb x, Show that (d^2y)/(dx^2)-2a(dy)/(...
Here you can see the derivative f'(x) and the second derivative f''(x) of some common functions.Notice how the slope of each function is the y-value of the derivative plotted below it.For example, move to where the sin(x) function slope flattens out (slope=0), then see that the...
Find the derivative of the function. y = sqrt( 1+ 2e^3x) Find the derivative of the function. \\ y = \frac{1 }{ 2} x^2 \sqrt {9 - x^2} 12) Find the derivative of the function y = \int_{\sqrt{x^{x^3}6 \sqrt 7 sin (t) dt. y'= Find the derivative of the...