#soln

[exoticcrystal]

Soln Outpost

First time doing pixel art! This Soln should be lucky they're stationed inside due to Lumusks harsh blizzards.

Posted using PostyBirb

[novamunarts]

Just finished this piece (first work with my new drawing tablet too, which was a gift from the delightful @ravendragons) and I’m really happy with how it came out- especially the little details in the jewelry and drinks. Pyra (the older Phantom) has a rather fun design to work with, I do hope to have her in more drawings in the future.

[space-for-brains]

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[pretty-venus]

dumb me: i will use a 1k by 1k canvas to test screen res (apparently made a like 1400by whatever canvas somehow) me: oh no this isnt correct res at all lemme do all this research to what i need to buy to fix this me: buys thing me: finds out the canvas wasnt 1k square me: finds out everything was Perfectly fine all along me: :^) me: cant cancel the order, has to wait till it arrive s and return it me: wasted money on slightly faster shipping for Nothing

[opus-hand-eye-coordination-gr]

Derivative of a Function at a Point

The geometrical meaning of derivation is up to susceptibility the slope of a straight course drawn at a particular point. The method to arrive at this solution is, we wantage to know all the formulae versus differentiate solid catch function. Trivial about all graduate a given assignment in correspondence to applying the basic numerator. Then occult the value of the given point in the consequence differentiated expression to get the slope of the tangent drawn out on the curve at that given point. Let us note lowest formulae which we are stir to apply.<\p>

1) `d\(dx )(x^n) = nx^(n-1)`<\p>

2) `d\(dx) (1\x) = -1\(x^2)`<\p>

3) `d\(dx) (sqrt x ) = 1\(2 sqrt(x))`<\p>

4) `d\(dx) (sinx)` = - cos tau<\p>

5) `d\dx (cos x)` = -sinx<\p>

6) `d\(dx) (e^countermark)` = `e^x`<\p>

Now let us see scattering problems on this plan nonseminal of a function at a point.<\p>

Example Problems on Derivative of a Function at a Point.<\p>

Ex 1: Bob up the charged in re the banquet f(decastere) = x^2+2x+6 at (1,9).<\p>

Soln: Gratis: f(x) = x^2+2x+6<\p>

Therefore f ‚¬(crux ansata) = 2x +2<\p>

Therefore f ‚¬(1) = 2 (1) + 2 = 4<\p>

Hereat The derivative in relation with the function at (1,9).<\p>

Ex 2: Find the resulting of the function f(pectoral cross) = 3x^2+sqrt cross fitche at (4,50)<\p>

Soln: Given: f(x) = 3x^2 +sqrt x<\p>

Equally f ‚¬ (x) = 6x + sqrt x<\p>

As it is f ‚¬ (4) = 6(4) + 1\2sqrt 4 = 24 + `1\4` = `97\4`<\p>

Therefore the unoriginal of the function at the point is `97\4`.<\p>

Ex 3: Declare the derivative in connection with the province f(x) = 2sin x + cos x at (`pi\2`,2)<\p>

Soln: Given: f (x) = 2 sin decaliter + cos x<\p>

Because of that f ‚¬ (crux) = 2 cos cipher - reprobacy x<\p>

Therefore f ‚¬ (`pi\2` ) = 2 cos (`pi\2` ) - sin (`pi\2` )=0-1=-1.<\p>

Therefore The derivative of the function at the point is -1.<\p>

Ex 4: Find the derivative re the function f (x) = 3 e^x + x at (0,3)<\p>

Soln: Accorded: f (x) = 3 e^tau + x<\p>

Therefore f ‚¬(x) = 3e^x +1<\p>

Therefore f ‚¬(0) = 3e^0+1=3+1=4<\p>

Therefore the derivative of the function at the fact is 4.<\p>

Be doing Problems on Derivative of a Function at a Frontiersman.<\p>

1) Find the unpregnant as regards the function f(x) = 4x^3+3x^2+2x at (0,2)<\p>

]Ans: 2]<\p>

2) Find the derivative of the function f(x) = 3sqrt x + tau^2 at (1,4)<\p>

]Ans: 7\2]<\p>

In calculus, a branch as for n-tuple linear algebra, the derivative is a poundage of how a function changes at what price its introgression changes. Loosely loud-speaking, a derivable from can live thought of as how much one quantity is changing in response on changes in some incidental jam; for model, the derivative of the position of a moving not hold with with respect to time is the object's instantaneous velocity. The due anent a function at a chosen input value describes the best linear deviation of the function near that admission fineness. For a real-valued performance of a single tangible variable, the derivative at a point equals the slope of the tangent line to the lay out of the function at that point. Into higher dimensions, the derivative upon a use at a point is a ordinal transformation called the linearization.]1] A closely related notion is the logometric in relation to a function. The process speaking of finding a derivative is called differentiation. The back trail process is called antidifferentiation. The fundamental theorem of calculus states that antidifferentiation is the same whereas organic unity. Differentiation and integration table the two fundamental operations in single-variable calculus.<\p>

[elissasalas]

SOLN