Derivative of sin(7^x)

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   / x\
sin\7 /

\sin{\left(7^{x} \right)}

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Detail solution

Let $u = 7^{x}$ .
The derivative of sine is cosine:

$\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} 7^{x}$ :
1. $\frac{d}{d x} 7^{x} = 7^{x} \log{\left(7 \right)}$
The result of the chain rule is:

$7^{x} \log{\left(7 \right)} \cos{\left(7^{x} \right)}$

The answer is:

7^{x} \log{\left(7 \right)} \cos{\left(7^{x} \right)}

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 x    / x\       
7 *cos\7 /*log(7)

7^{x} \log{\left(7 \right)} \cos{\left(7^{x} \right)}

Simplify

The second derivative [src]

 x    2    /   x    / x\      / x\\
7 *log (7)*\- 7 *sin\7 / + cos\7 //

7^{x} \left(- 7^{x} \sin{\left(7^{x} \right)} + \cos{\left(7^{x} \right)}\right) \log{\left(7 \right)}^{2}

Simplify

The third derivative [src]

 x    3    /   2*x    / x\      x    / x\      / x\\
7 *log (7)*\- 7   *cos\7 / - 3*7 *sin\7 / + cos\7 //

7^{x} \left(- 7^{2 x} \cos{\left(7^{x} \right)} - 3 \cdot 7^{x} \sin{\left(7^{x} \right)} + \cos{\left(7^{x} \right)}\right) \log{\left(7 \right)}^{3}

Simplify

The graph