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

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

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

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

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

2 e^{x^{2}} x cos (e^{x^{2}}) cos (x) - sin (x) sin (e^{x^{2}})

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sin (e^{x^{2}}), g = cos (x)

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

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

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

= cos (e^{x^{2}}) e^{x^{2}} \cdot 2 x cos (x) + (- sin (x)) sin (e^{x^{2}})

Simplify

= 2 e^{x^{2}} x cos (e^{x^{2}}) cos (x) - sin (x) sin (e^{x^{2}})

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