Math Doubts

Derivative of sinx

Formula

$\dfrac{d}{dx}{\, (\sin{x})} \,=\, \cos{x}$

The derivative or differentiation of sin function with respect to a variable is equal to cosine. So, it is read as the derivative of $\sin{x}$ with respect to $x$ is equal to $\cos{x}$.

Introduction

If $x$ is a variable, then the sine function is written as $\sin{x}$ in mathematics. The differentiation of the sin function with respect to $x$ is written mathematically as follows.

$\dfrac{d}{dx}{\, (\sin{x})}$

The derivative of $\sin{x}$ with respect to $x$ can also be expressed as $\dfrac{d{\,(\sin{x})}}{dx}$. It is also simply written as ${(\sin{x})}’$ mathematically in calculus.

Other form

The derivative of the sin function can be written in terms of any variable.

$(1) \,\,\,$ $\dfrac{d}{dm}{\, (\sin{m})} \,=\, \cos{m}$

$(2) \,\,\,$ $\dfrac{d}{dy}{\, (\sin{y})} \,=\, \cos{y}$

Proof

Learn how to derive the derivative of the sine function by first principle in differential calculus.

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