Answer to: Find the anti-derivative of int frac{5 + sqrt{x} + x}{x} dx By signing up, you'll get thousands of step-by-step solutions to your...
Given a continuous function {eq}f(x), {/eq} an antiderivative of {eq}f {/eq} is any function {eq}F(x) {/eq} such that {eq}F'(x) = f(x). {/eq} For a given function f, if we can find one antiderivative, then we can find a family of antiderivatives o...
If you can use the chain rule and the fact that the derivative of exex is exex and the fact that ln(x)ln(x) is differentiable, then we have: ddxx=1ddxx=1 ddxeln(x)=eln(x)ddxln(x)=1ddxeln(x)=eln(x)ddxln(x)=1 eln(x)ddxln(x)=1eln(x)ddxln(x)...
derivativeoff(x)=4sin(x)+2xx,x=2 Description Find the value of a function derivative at a given point Related Symbolab blog posts Advanced Math Solutions – Derivative Calculator, Implicit Differentiation We’ve covered methods and rules to differentiate functions of the form y=f(x), where y...
DerivativeDifferentiationIntegralDefiniteintegralIndefiniteintegralAntiderivative 导数微分积分定积分不定积分不定积分 Definitionofthederivative Thederivativeoffatxisgivenby f(xx)f(x)f(x)limx0x 'Afunctionisdifferentiableatxifitsderivativeexistsatx.Theprocessoffindingderivativesiscalled...
ln(x)is−∞andthelimitlim x→∞ ln(x)is+∞.Notethatlngoesoffto+∞at∞ eventhoughitsderivativegoestozeroasx→+∞. (4)Thederivativeofln(x)is1/xandthederivativeofln(kx)isalso1/x.Thederivativeofln(x r )is r/x. (5)Theantiderivativeof1/xisln|x|+C.Whatthisreallymeansisthattheantide...
dx ln(|x|)=1 x d dx (sin(x))=cos(x)d dx (cos(x))=−sin(x)d dx (tan(x))=sec2(x)d dx (csc(x))=−csc(x)cot(x)d dx (sec(x))=sec(x)tan(x)d dx (cot(x))=−csc2(x)d dx (sin−1(x))=1 √ 1−x2 d dx (cos−1(x)=−1 √ 1−x2 d dx...
Find the most general form of the indefinite integral. integral {ln 8 x} / {x} dx Find the following anti derivatives: Integral of (2x + 7)^3 dx. Find the antiderivative of the function: {x square root x + 3 x} / {x^2}. ...
first i thought he was asking why the integral of e^x was e^x? Then i reread it and saw that he was actually asking why e^x=(e^x)' After this i did the pathetic "antiderivative of a function is equal to the integral, which is equal to the area under the curve business." Bu...
Compute the derivative of the following function. u (t^4 - 2 t) Suppose that the derivative of a function is df over dx = 1 over 18x - 9. Find any antiderivative of the above function. Compute the first derivative of the following function: ...