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人気のある微分積分 >

d/(dy)(cos(xy))

解

\frac{d}{d y} (cos (x y))

解

- sin (x y) x

解答ステップ

\frac{d}{d y} (cos (x y))

x

を定数として扱う

連鎖法則を適用:

- sin (x y) \frac{d}{d y} (x y)

= - sin (x y) \frac{d}{d y} (x y)

\frac{d}{d y} (x y) = x

= - sin (x y) x

人気の例

(dy)/(dt)= t/(t^2y+y)

\frac{d y}{d t} = \frac{t}{t ^{2} y + y}

(d^2)/(dx^2)((x^2+6)^4)

\frac{d ^{2}}{d x ^{2}} ((x^{2} + 6)^{4})

integral of x^{(-1)/2}

\int x^{\frac{- 1}{2}} d x

integral of (cos^2(x))/(sin^4(x))

\int \frac{cos ^{2} ( x )}{sin ^{4} ( x )} d x

sum from n=3 to infinity of 5/(9^n)

n = 3 \sum \infty \frac{5}{9 ^{n}}