What is the derivative of (3+tan(x)^x) ?

The derivative of (3+tan(x)^x) is (ln(3+tan(x))+(xsec^2(x))/(3+tan(x)))(3+tan(x))^x

What is the first derivative of (3+tan(x)^x) ?

The first derivative of (3+tan(x)^x) is (ln(3+tan(x))+(xsec^2(x))/(3+tan(x)))(3+tan(x))^x

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\frac{d}{d x} ((3 + tan (x))^{x})

(ln (3 + tan (x)) + \frac{x sec ^{2} ( x )}{3 + tan ( x )}) (3 + tan (x))^{x}

Solution steps

\frac{d}{d x} ((3 + tan (x))^{x})

Apply exponent rule:

a^{b} = e^{b l n (a)}

(3 + tan (x))^{x} = e^{x l n (3 + t a n (x))}

= \frac{d}{d x} (e^{x l n (3 + t a n (x))})

Apply the chain rule:

e^{x l n (3 + t a n (x))} \frac{d}{d x} (x ln (3 + tan (x)))

= e^{x l n (3 + t a n (x))} \frac{d}{d x} (x ln (3 + tan (x)))

\frac{d}{d x} (x ln (3 + tan (x))) = ln (3 + tan (x)) + \frac{x sec ^{2} ( x )}{3 + tan ( x )}

= e^{x l n (3 + t a n (x))} (ln (3 + tan (x)) + \frac{x sec ^{2} ( x )}{3 + tan ( x )})

e^{x l n (3 + t a n (x))} = (3 + tan (x))^{x}

= (ln (3 + tan (x)) + \frac{x sec ^{2} ( x )}{3 + tan ( x )}) (3 + tan (x))^{x}

\frac{\partial}{\partial x} (\frac{( t - y )}{8 t + 3 y})

y^{^{''}} = 1 - 2 y^{^{'}}

5 t

\int \frac{∣ x ∣}{x} d x

\int \frac{x arctan ( x )}{1 + x ^{2}} d x

What is the derivative of (3+tan(x)^x) ?
The derivative of (3+tan(x)^x) is (ln(3+tan(x))+(xsec^2(x))/(3+tan(x)))(3+tan(x))^x
What is the first derivative of (3+tan(x)^x) ?
The first derivative of (3+tan(x)^x) is (ln(3+tan(x))+(xsec^2(x))/(3+tan(x)))(3+tan(x))^x