Derivatives of trigonometric functions Calculator

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Example

Solved Problems

Difficult Problems

Solved example of derivatives of trigonometric functions

$\frac{d}{dx}\cos\left(3x^2+x-5\right)$

Multiply $3$ times $[b]$

$\frac{d}{dx}\left(\cos\left(0x^2+x-5\right)\right)$

Any expression multiplied by $0$ is equal to $0$

$\frac{d}{dx}\left(\cos\left(-5+x\right)\right)$

Simplifying

$\frac{d}{dx}\left(\cos\left(-5+x\right)\right)$

The derivative of the cosine of a function is equal to minus the sine of the function times the derivative of the function, in other words, if $f(x) = \cos(x)$, then $f'(x) = -\sin(x)\cdot D_x(x)$

$-\sin\left(-5+x\right)\frac{d}{dx}\left(-5+x\right)$

The derivative of a sum of two functions is the sum of the derivatives of each function

$-\sin\left(-5+x\right)\left(\frac{d}{dx}\left(-5\right)+\frac{d}{dx}\left(x\right)\right)$

The derivative of the constant function ($-5$) is equal to zero

$-\sin\left(-5+x\right)\frac{d}{dx}\left(x\right)$

The derivative of the linear function is equal to $1$

$-\sin\left(-5+x\right)$

Final Answer