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人気のある微分積分 >

(\partial)/(\partial y)(e^{sin(x+y)})

解

\frac{\partial}{\partial y} (e^{s i n (x + y)})

解

e^{s i n (x + y)} cos (x + y)

解答ステップ

\frac{\partial}{\partial y} (e^{s i n (x + y)})

x

を定数として扱う

連鎖法則を適用:

e^{s i n (x + y)} \frac{\partial}{\partial y} (sin (x + y))

= e^{s i n (x + y)} \frac{\partial}{\partial y} (sin (x + y))

\frac{\partial}{\partial y} (sin (x + y)) = cos (x + y)

= e^{s i n (x + y)} cos (x + y)

人気の例

tangent f(x)=1+4csc(x),\at x=-pi/3

t an g e n t f (x) = 1 + 4 csc (x), at x = - \frac{π}{3}

sum from n=1 to infinity of 2/(3n+10)

n = 1 \sum \infty \frac{2}{3 n + 10}

integral from 1 to 2 of 4xsqrt(4x^2+4)

\int_{1}^{2} 4 x 4 x^{2} + 4 d x

integral of (3x^4-5x^2+6x)

\int (3 x^{4} - 5 x^{2} + 6 x) d x

sum from n=1 to infinity of 8

n = 1 \sum \infty 8