Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Find the derivative
- Find the derivative using the definition
- Find the derivative using the product rule
- Find the derivative using the quotient rule
- Find the derivative using logarithmic differentiation
- Find the derivative
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
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The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$
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$\frac{1}{2}\left(\frac{e^{5x}\sin\left(e^{\tan\left(e^x\right)}\right)}{2}\right)^{-\frac{1}{2}}\frac{d}{dx}\left(\frac{e^{5x}\sin\left(e^{\tan\left(e^x\right)}\right)}{2}\right)$
Learn how to solve problems step by step online. Find the derivative of ((e^(5x)sin(e^tan(e^x)))/2)^(1/2). The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Since the exponent is negative, we can invert the fraction. The derivative of a function multiplied by a constant (\frac{1}{2}) is equal to the constant times the derivative of the function. When multiplying two powers that have the same base (\frac{1}{2}), you can add the exponents.