derivative of cos(2x^2-3) — step-by-step solution

Let's perform the differentiation:

\frac{d}{d x} (\cos (2 x^{2} - 3))

Apply the differentiation rule:

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

with f =

2 x^{2} - 3

ⓘ The derivative of cos(x) is -sin(x):

\frac{d}{d x} (\cos (2 x^{2} - 3))

- \frac{d}{d x} (2 x^{2} - 3) \cdot \sin (2 x^{2} - 3)

- \frac{d}{d x} (2 x^{2} - 3) \cdot \sin (2 x^{2} - 3)

ⓘ The derivative of a sum is the sum of the derivatives:

\frac{d}{d x} (2 x^{2} - 3)

\frac{d}{d x} (2 x^{2}) + 0

- (\frac{d}{d x} (2 x^{2}) + 0) \cdot \sin (2 x^{2} - 3)

ⓘ Adding 0 changes nothing:

\frac{d}{d x} (2 x^{2}) + 0

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

■A constant factor stays in front of the derivative, (k*u)' = k*u':

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

2 \cdot \frac{d}{d x} (x^{2})

■The derivative of x^n is n*x^(n-1):

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

2 x

- 2 \cdot 2 x \cdot \sin (2 x^{2} - 3)

ⅰ

2 \cdot 2

4

▶Derivative:

- 4 x \cdot \sin (2 x^{2} - 3)