Since99isconstantwith respect toxx, thederivativeof9x29x2with respect toxxis9ddx[1x2]9ddx[1x2]. 9ddx[1x2]9ddx[1x2] Apply basic rules ofexponents. Tap for more steps... Rewrite1x2as(x2)-1. 9ddx[(x2)-1] thein(x2)-1. ...
Sinceaaisconstantwith respect toxx, thederivativeofaxaxwith respect toxxisaddx[x]addx[x]. addx[x]addx[x] Differentiate using thePower Rulewhich states thatddx[xn]ddx[xn]isnxn−1nxn-1wheren=1n=1. a⋅1a⋅1 Multiplyaaby11.
Since55isconstantwith respect toxx, thederivativeof5x25x2with respect toxxis5ddx[x2]5ddx[x2]. 5ddx[x2]5ddx[x2] Differentiate using thePower Rulewhich states thatddx[xn]ddx[xn]isnxn−1nxn-1wheren=2n=2. 5(2x)5(2x) Multiply22by55. ...
Since22isconstantwith respect toxx, thederivativeof2x32x3with respect toxxis2ddx[x3]2ddx[x3]. 2ddx[x3]2ddx[x3] Differentiate using thePower Rulewhich states thatddx[xn]ddx[xn]isnxn−1nxn-1wheren=3n=3. 2(3x2)2(3x2) Multiply33by22. ...
f(x)=4√x4x,a=19a=19 Usen√ax=axnaxn=axnto rewrite√xxasx12x12. ddx[4x12]ddx[4x12] Since44isconstantwith respect toxx, thederivativeof4x124x12with respect toxxis4ddx[1x12]4ddx[1x12]. 4ddx[1x12]4ddx[1x12] Apply basic rules ofexponents. ...
Algebra Examples 4πr24πr2 Since4π4πisconstantwith respect torr, thederivativeof4πr24πr2with respect torris4πddr[r2]4πddr[r2]. 4πddr[r2]4πddr[r2] Differentiate using thePower Rulewhich states thatddr[rn]ddr[rn]isnrn−1nrn-1wheren=2n=2. ...
A critical point of a function of a real variable is any value in the domain where either the function is not differentiable or its derivative is 00. cross multiply In a proportion, to rewrite the equation so that the product of the means equals the product of the extremes. cross product...
Sinceyzyzisconstantwith respect toxx, thederivativeofxyzxyzwith respect toxxisyzddx[x]yzddx[x]. yzddx[x]yzddx[x] Differentiate using thePower Rulewhich states thatddx[xn]ddx[xn]isnxn−1nxn-1wheren=1n=1. yz⋅1yz⋅1 Multiplyyyby11. ...
ex+e−x2ex+e-x2 Sinceex+e−x2ex+e-x2isconstantwith respect toee, thederivativeofex+e−x2ex+e-x2with respect toeeis00. f'(e)=0f′(e)=0 Since00isconstantwith respect toee, thederivativeof00with respect toeeis00.
Thederivativeofcos(x)cos(x)with respect toxxis−sin(x)-sin(x). −sin(x)-sin(x) ( ) | [ ] √ ≥ ∫ 7 8 9 ≤ ° θ 4 5 6 / ^ × > π