Find the derivative of this function using chain rule or product rule I am trying to find the derivative of $f(x)$$=$$10^{x^2+2}$
Can anybody help me try to solve this through the chain rule?
I have tried using the chain rule and exponent rule I figured out that
$f(x)=10^x$ the derivative is $f'(x)=ln(10)10^x$
$g(x) = x^2+2$ the derivative is $g'(x) = 2x$
Hence my answer for this derivative of function f(x) was
$f'(x) = (2x)(ln(10))(10^{x^2+2})$
however on the calculator/wolfram alpha it says that the answer is

I am unsure what the next steps to take to confirm which one is the right derivative.
You did it correctly and got the same answer as Wolfram did.
When Wolfram writes &quot;$\log$&quot; it means the natural log.  (That's common, but confusing as hell, practice).
Wolfram wrote $2^{x^2+3}\times 5^{x^2 + 2}x \log 10$ and meant $2^{x^2+3}\times 5^{x^2 + 2}x \ln 10$ and you got $(2x)(ln(10))(10^{x^2+2})$.
what's the difference?
Actually nothing.
$2^{x^2+3}\times 5^{x^2 + 2}x \ln 10 =$
$2\cdot 2^{x^2 + 2}\times 5^{x^2 + 2} x \ln 10=$
$2(2\times 5)^{x^2 + 2}  x\ln 10=$
$2\cdot 10^{x^2+2} x \ln 10$
which, order and parenthesis aside, is exactly what you got.
So you did jes' fine.
You did it correctly and got the same answer as Wolfram did.
When Wolfram writes &quot;$\log$&quot; it means the natural log.  (That's common, but confusing as hell, practice).
Wolfram wrote $2^{x^2+3}\times 5^{x^2 + 2}x \log 10$ and meant $2^{x^2+3}\times 5^{x^2 + 2}x \ln 10$ and you got $(2x)(ln(10))(10^{x^2+2})$.
what's the difference?
Actually nothing.
$2^{x^2+3}\times 5^{x^2 + 2}x \ln 10 =$
$2\cdot 2^{x^2 + 2}\times 5^{x^2 + 2} x \ln 10=$
$2(2\times 5)^{x^2 + 2}  x\ln 10=$
$2\cdot 10^{x^2+2} x \ln 10$
which, order and parenthesis aside, is exactly what you got.
So you did jes' fine.