What is the derivative of e^{sin(x^2}) ?

The derivative of e^{sin(x^2}) is e^{sin(x^2)}cos(x^2)*2x

What is the first derivative of e^{sin(x^2}) ?

The first derivative of e^{sin(x^2}) is e^{sin(x^2)}cos(x^2)*2x

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

y^{^{'}} - 7 y = sin (2 x)

y = 1 + x - 4 x^{\frac{1}{2}}

arctan (\frac{1 + x}{1 - x})

2 + \frac{d y}{d x} = 2 x + y

\frac{d}{d x} (\frac{in x}{x})

What is the derivative of e^{sin(x^2}) ?
The derivative of e^{sin(x^2}) is e^{sin(x^2)}cos(x^2)*2x
What is the first derivative of e^{sin(x^2}) ?
The first derivative of e^{sin(x^2}) is e^{sin(x^2)}cos(x^2)*2x