What is the derivative of cos(x)sin(x^2) ?

The derivative of cos(x)sin(x^2) is -sin(x)sin(x^2)+2xcos(x^2)cos(x)

What is the first derivative of cos(x)sin(x^2) ?

The first derivative of cos(x)sin(x^2) is -sin(x)sin(x^2)+2xcos(x^2)cos(x)

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

\int_{0}^{8} t e^{- t} d t

2 y^{^{'}} + y = 1

\int_{0}^{2} x^{2} (1 + 2 x^{3})^{3} d x

\int \frac{5}{( x - 1 ) ^{2}} d x

\int \frac{x + 5}{2 x ^{3} - 8 x} d x

What is the derivative of cos(x)sin(x^2) ?
The derivative of cos(x)sin(x^2) is -sin(x)sin(x^2)+2xcos(x^2)cos(x)
What is the first derivative of cos(x)sin(x^2) ?
The first derivative of cos(x)sin(x^2) is -sin(x)sin(x^2)+2xcos(x^2)cos(x)