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Exercise

$\frac{d}{dx}\left(x^{siny}\right)=\left(y^{cosx}\right)$

Step-by-step Solution

1

The derivative $\frac{d}{dx}\left(x^{\sin\left(y\right)}\right)$ results in $\left(\cos\left(x^{\sin\left(y\right)}\right)\ln\left(x\right)+\frac{\sin\left(x^{\sin\left(y\right)}\right)}{x}\right)x^{\sin\left(y\right)}$

$\left(\cos\left(x^{\sin\left(y\right)}\right)\ln\left(x\right)+\frac{\sin\left(x^{\sin\left(y\right)}\right)}{x}\right)x^{\sin\left(y\right)}=y^{\cos\left(x\right)}$

Final answer to the exercise

$\left(\cos\left(x^{\sin\left(y\right)}\right)\ln\left(x\right)+\frac{\sin\left(x^{\sin\left(y\right)}\right)}{x}\right)x^{\sin\left(y\right)}=y^{\cos\left(x\right)}$

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