Différenciation avancée Calculator

Here, we show you a step-by-step solved example of différenciation avancée. This solution was automatically generated by our smart calculator:

Apply the formula: $\frac{d}{dx}\left(a^b\right)$$=y=a^b$, where $d/dx=\frac{d}{dx}$, $a=x$, $b=7\sin\left(x\right)$, $a^b=x^{7\sin\left(x\right)}$ and $d/dx?a^b=\frac{d}{dx}\left(x^{7\sin\left(x\right)}\right)$

Apply the formula: $y=a^b$$\to \ln\left(y\right)=\ln\left(a^b\right)$, where $a=x$ and $b=7\sin\left(x\right)$

Apply the formula: $\ln\left(x^a\right)$$=a\ln\left(x\right)$, where $a=7\sin\left(x\right)$

Apply the formula: $\ln\left(y\right)=x$$\to \frac{d}{dx}\left(\ln\left(y\right)\right)=\frac{d}{dx}\left(x\right)$, where $x=7\sin\left(x\right)\ln\left(x\right)$

Apply the formula: $\frac{d}{dx}\left(cx\right)$$=c\frac{d}{dx}\left(x\right)$

Apply the formula: $\frac{d}{dx}\left(ab\right)$$=\frac{d}{dx}\left(a\right)b+a\frac{d}{dx}\left(b\right)$, where $d/dx=\frac{d}{dx}$, $ab=\sin\left(x\right)\ln\left(x\right)$, $a=\sin\left(x\right)$, $b=\ln\left(x\right)$ and $d/dx?ab=\frac{d}{dx}\left(\sin\left(x\right)\ln\left(x\right)\right)$

Apply the trigonometric identity: $\frac{d}{dx}\left(\sin\left(\theta \right)\right)$$=\frac{d}{dx}\left(\theta \right)\cos\left(\theta \right)$

Apply the formula: $\frac{d}{dx}\left(x\right)$$=1$

Apply the formula: $\frac{a}{b}=c$$\to a=cb$, where $a=y^{\prime}$, $b=y$ and $c=7\left(\cos\left(x\right)\ln\left(x\right)+\frac{\sin\left(x\right)}{x}\right)$

Substitute $y$ for the original function: $x^{7\sin\left(x\right)}$

The derivative of the function results in