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

The derivative of e^{cos(x^2}) is -2e^{cos(x^2)}xsin(x^2)

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

The first derivative of e^{cos(x^2}) is -2e^{cos(x^2)}xsin(x^2)

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\frac{d}{d x} (e^{c o s (x^{2})})

- 2 e^{c o s (x^{2})} x sin (x^{2})

Solution steps

\frac{d}{d x} (e^{c o s (x^{2})})

Apply the chain rule:

e^{c o s (x^{2})} \frac{d}{d x} (cos (x^{2}))

= e^{c o s (x^{2})} \frac{d}{d x} (cos (x^{2}))

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

= e^{c o s (x^{2})} (- sin (x^{2}) \cdot 2 x)

Simplify

= - 2 e^{c o s (x^{2})} x sin (x^{2})

\frac{d}{d x} (tan (e^{2 x}) + e^{t a n (2 x)})

x \to - 1 - lim (\frac{1}{( x + 1 ) ^{2}})

\int_{0}^{\infty} 5^{- x} d x

\int sec^{4} (x) d x

f (t) = t^{4}

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