What is the derivative of y=5^{tan(5x)} ?

The derivative of y=5^{tan(5x)} is ln(5)*5^{tan(5x)+1}sec^2(5x)

What is the first derivative of y=5^{tan(5x)} ?

The first derivative of y=5^{tan(5x)} is ln(5)*5^{tan(5x)+1}sec^2(5x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

y = 5^{t a n (5 x)}

ln (5) \cdot 5^{t a n (5 x) + 1} sec^{2} (5 x)

Solution steps

\frac{d}{d x} (5^{t a n (5 x)})

Apply exponent rule:

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

5^{t a n (5 x)} = e^{t a n (5 x) l n (5)}

= \frac{d}{d x} (e^{t a n (5 x) l n (5)})

Apply the chain rule:

e^{t a n (5 x) l n (5)} \frac{d}{d x} (tan (5 x) ln (5))

= e^{t a n (5 x) l n (5)} \frac{d}{d x} (tan (5 x) ln (5))

\frac{d}{d x} (tan (5 x) ln (5)) = ln (5) sec^{2} (5 x) \cdot 5

= e^{t a n (5 x) l n (5)} ln (5) sec^{2} (5 x) \cdot 5

Simplify

e^{t a n (5 x) l n (5)} ln (5) sec^{2} (5 x) \cdot 5 : ln (5) \cdot 5^{t a n (5 x) + 1} sec^{2} (5 x)

= ln (5) \cdot 5^{t a n (5 x) + 1} sec^{2} (5 x)

\int \frac{4}{y} d y

x^{3} + 1

x \to - \infty lim (3 x + 9 x^{2} + 7 x - 8)

\int 16 x d x

\int \frac{40 x}{5 x ^{2} + e} d x

What is the derivative of y=5^{tan(5x)} ?
The derivative of y=5^{tan(5x)} is ln(5)*5^{tan(5x)+1}sec^2(5x)
What is the first derivative of y=5^{tan(5x)} ?
The first derivative of y=5^{tan(5x)} is ln(5)*5^{tan(5x)+1}sec^2(5x)