What is (\partial)/(\partial x)(e^{sin(x^2)}) ?

The answer to (\partial)/(\partial x)(e^{sin(x^2)}) is e^{sin(x^2)}cos(x^2)*2x

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(\partial)/(\partial x)(e^{sin(x^2)})

\frac{\partial}{\partial x} (e^{s i n (x^{2})})

e^{s i n (x^{2})} cos (x^{2}) \cdot 2 x

Solution steps

\frac{\partial}{\partial x} (e^{s i n (x^{2})})

Apply the chain rule:

e^{s i n (x^{2})} \frac{\partial}{\partial x} (sin (x^{2}))

= e^{s i n (x^{2})} \frac{\partial}{\partial x} (sin (x^{2}))

\frac{\partial}{\partial x} (sin (x^{2})) = cos (x^{2}) \cdot 2 x

= e^{s i n (x^{2})} cos (x^{2}) \cdot 2 x

\int \frac{5 arcsin ( x )}{x ^{2}} d x

x^{3} y^{^{'}} + 2 x^{2} y = - 3 cos (3 x) y^{- \frac{1}{2}}

y^{^{'}} + 2 x y - 6 = 0

\frac{d}{d x} (\frac{2 x}{4})

\frac{s}{s ^{2} + 2}

What is (\partial)/(\partial x)(e^{sin(x^2)}) ?
The answer to (\partial)/(\partial x)(e^{sin(x^2)}) is e^{sin(x^2)}cos(x^2)*2x