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Popular >

derivative of sin(9x+(sin(9x))^2)

Solution

\frac{d}{d x} (sin (9 x) + (sin (9 x))^{2})

Solution

cos (9 x) \cdot 9 + 18 sin (9 x) cos (9 x)

Solution steps

\frac{d}{d x} (sin (9 x) + (sin (9 x))^{2})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (sin (9 x)) + \frac{d}{d x} ((sin (9 x))^{2})

\frac{d}{d x} (sin (9 x)) = cos (9 x) \cdot 9

\frac{d}{d x} ((sin (9 x))^{2}) = 18 sin (9 x) cos (9 x)

= cos (9 x) \cdot 9 + 18 sin (9 x) cos (9 x)

Graph

Popular Examples

derivative of f(2x)=5x-3 derivative of

f (2 x) = 5 x - 3

(\partial)/(\partial x)(x+sqrt(y))

\frac{\partial}{\partial x} (x + y)

(t + y + 1) d t - d y = 0

derivative of f(x)=2x-4 derivative of

f (x) = 2 x - 4

derivative of ((x+1/(x-1))^4)

\frac{d}{d x} ((\frac{x + 1}{x - 1})^{4})

Frequently Asked Questions (FAQ)

What is the derivative of sin(9x+(sin(9x))^2) ?
The derivative of sin(9x+(sin(9x))^2) is cos(9x)*9+18sin(9x)cos(9x)
What is the first derivative of sin(9x+(sin(9x))^2) ?
The first derivative of sin(9x+(sin(9x))^2) is cos(9x)*9+18sin(9x)cos(9x)