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

The derivative of e^{sin(cos(x^n)}) is -ne^{sin(cos(x^n))}x^{n-1}sin(x^n)cos(cos(x^n))

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

The first derivative of e^{sin(cos(x^n)}) is -ne^{sin(cos(x^n))}x^{n-1}sin(x^n)cos(cos(x^n))

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

- n e^{s i n (c o s (x^{n}))} x^{n - 1} sin (x^{n}) cos (cos (x^{n}))

Solution steps

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

Apply the chain rule:

e^{s i n (c o s (x^{n}))} \frac{d}{d x} (sin (cos (x^{n})))

= e^{s i n (c o s (x^{n}))} \frac{d}{d x} (sin (cos (x^{n})))

\frac{d}{d x} (sin (cos (x^{n}))) = - n x^{n - 1} sin (x^{n}) cos (cos (x^{n}))

= e^{s i n (c o s (x^{n}))} (- n x^{n - 1} sin (x^{n}) cos (cos (x^{n})))

Simplify

= - n e^{s i n (c o s (x^{n}))} x^{n - 1} sin (x^{n}) cos (cos (x^{n}))

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\frac{d y}{d x} = \frac{( 2 x ( y - 1 ) )}{x ^{2} + 3}, y (1) = 9

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What is the derivative of e^{sin(cos(x^n)}) ?
The derivative of e^{sin(cos(x^n)}) is -ne^{sin(cos(x^n))}x^{n-1}sin(x^n)cos(cos(x^n))
What is the first derivative of e^{sin(cos(x^n)}) ?
The first derivative of e^{sin(cos(x^n)}) is -ne^{sin(cos(x^n))}x^{n-1}sin(x^n)cos(cos(x^n))