Find ᵈʸ⁄dₓ, if y = x^{tanx}.
In x^{tanx}, we have varoiable x is in exponent.
To find the derivative of a term which contain variable in exponent, we have to take natural logarithm on both sides. Then, we have to use the rules of logarithm and find the derivative.
y = x^{tanx}
Take natural logarithm on both sides.
ln(y) = ln(x^{tanx})
ln(y) = tanx ⋅ ln(x)
Now, we have find the derivative on both sides with respect to x.
To find the derivative of ln(y) with respect to x, we have to use use chain rule.
To find the derivative tanx⋅ln(x) on the right side, we have to use product rule.
Multiply both sides by y.
Substitute y = x^{tanx}.
Therefore,
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
May 26, 23 12:27 PM
May 21, 23 07:40 PM
May 20, 23 10:53 PM