Turunan pertama dari f(x) = √(x^2+ 1)

Tentukan f(x)^’ dari f(x) = √(x^2+ 1) !

Jawab :

Gunakan aturan rantai

Misalkan: z = x^2+ 1 → dz/dx=2x

Maka : y = √(z ) → dy/dz= 1/(2√(z ))= 1/(2√(x^2+ 1 ))

Maka : f(x)^’= dy/dx=( dy/dz)( dz/dx)=(1/(2√(x^2+ 1 )))(2x) = x/√(x^2+ 1 )

for more detailed writing click on the following link Tentukan f(x)^’ dari f(x) = √(x^2+ 1)

f(x) = x^2 sin⁡x tan⁡x

Tentukanlah turunan  fungsi berikut ! f(x) = x^2 sin⁡x tan⁡x

Jawab:

f(x)^’ = d(x^2)/dx sin⁡x tan⁡x + x^2 d(sin⁡x)/dx (tan⁡x)+ x^2 (sinx) d(tan⁡x)/dx

f(x)^’=(2x) sin⁡x tan⁡x  + x^2 (cos⁡x)tan⁡x+ x^2 sin⁡x (sec^2 x)

f(x)^’=x(2sinxtanx+xcosxtanx+xsinxsec^2 x)

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Tentukanlah turunan setiap fungsi berikut ! f(x) = x^2 sin⁡x tan⁡x

f(x) = x e^x csc ⁡x

Tentukanlah turunan fungsi berikut ! f(x) = x e^x csc⁡x

Jawab:

f(x)^’ = (d(x))/dx e^x csc⁡x + x(d(e^x))/dx csc⁡x + xe^x (d(csc⁡x))/dx

f(x)^’=(1) e^x csc⁡x + x(e^x)csc⁡x+ x e^x (-csc⁡x cot⁡x)

f(x)^’= e^x csc⁡x+ x(e^x)csc⁡x-  x e^x csc⁡x cot⁡x

f(x)^’= e^x csc⁡x ( 1+x-x cot⁡x)

for more detailed writing click on the following link Tentukanlah turunan fungsi berikut ! f(x) = x e^x csc⁡x

(a) f(x) = √x sin⁡x (b) f(x) = csc x + e^x cot x

Turunkanlah setiap fungsi berikut !

(a) f(x) = √x sin⁡x

(b) f(x) = csc x + e^x cot x

\Jawab :

(a) f(x)^’ = (1/(2√x))(sin⁡x) +  (√x )( cos⁡x)= sin⁡x/(2√x) + √x cos⁡x f(x)^’ = (- csc x cot x) + [(e^x)(cot⁡x)+(e^x )(- csc^2x)]

(b) f(x)^’ = – csc x cot x + e^x cot x – e^x csc^2 x f(x)^’ = e^x (cot⁡x- csc^2x) – csc x cot x

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Turunkanlah setiap fungsi berikut ! f(x) = √x sin⁡x f(x) = csc x + e^x cot x

(a) f(x) = 3x^2- 2 cos⁡x (b) f(x) = sin x + 1/2 cot⁡x (c) f(x) = x^3 cos x Tentukan turunannya!

Turunkanlah setiap fungsi berikut !

(a) f(x) = 3x^2- 2 cos⁡x

(b) f(x) = sin x + 1/2 cot⁡x

(c) f(x) = x^3 cos x

Jawab :

(a) f(x)^’ = 6x + 2 sin x

(b)  f(x)^’ = cos x – 1/2 csc^2x

(c) f(x)^’ = (3x^2)(cos⁡x)+(x^3 )(-sin⁡x)= 3x^2 cos⁡x- x^3 sinx

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Turunkanlah setiap fungsi berikut ! f(x) = 3x^2- 2 cos⁡x f(x) = sin x + 1/2 cot⁡x f(x) = x^3 cos x