Solve f(x) = 7x cos(7x)

Evaluate

f (x) = 7 x cos (7 x)

Take the derivative of both sides

f^{'} (x) = \frac{d}{d x} (7 x cos (7 x))

Use differentiation rule \frac{d}{d x} (f (x) \times g (x)) = \frac{d}{d x} (f (x)) \times g (x) + f (x) \times \frac{d}{d x} (g (x))

f^{'} (x) = \frac{d}{d x} (7) \times x cos (7 x) + 7 \times \frac{d}{d x} (x) \times cos (7 x) + 7 x \times \frac{d}{d x} (cos (7 x))

Use \frac{d}{d x} (c) = 0 to find derivative

f^{'} (x) = 0 \times x cos (7 x) + 7 \times \frac{d}{d x} (x) \times cos (7 x) + 7 x \times \frac{d}{d x} (cos (7 x))

Calculate

f^{'} (x) = 0 + 7 \times \frac{d}{d x} (x) \times cos (7 x) + 7 x \times \frac{d}{d x} (cos (7 x))

Use \frac{d}{d x} x^{n} = n x^{n - 1} to find derivative

f^{'} (x) = 0 + 7 \times 1 \times cos (7 x) + 7 x \times \frac{d}{d x} (cos (7 x))

Calculate

f^{'} (x) = 0 + 7 cos (7 x) + 7 x \times \frac{d}{d x} (cos (7 x))

Calculate

More Steps

f^{'} (x) = 0 + 7 cos (7 x) + 7 x (- 7 sin (7 x))

Calculate

f^{'} (x) = 0 + 7 cos (7 x) - 49 x sin (7 x)

Solution

f^{'} (x) = 7 cos (7 x) - 49 x sin (7 x)

Function