What is the derivative of y=x^53^x ?

The derivative of y=x^53^x is 5x^4*3^x+3^xln(3)x^5

What is the first derivative of y=x^53^x ?

The first derivative of y=x^53^x is 5x^4*3^x+3^xln(3)x^5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

y = x^{5} 3^{x}

5 x^{4} \cdot 3^{x} + 3^{x} ln (3) x^{5}

Solution steps

\frac{d}{d x} (x^{5} \cdot 3^{x})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{5}, g = 3^{x}

= \frac{d}{d x} (x^{5}) 3^{x} + \frac{d}{d x} (3^{x}) x^{5}

\frac{d}{d x} (x^{5}) = 5 x^{4}

\frac{d}{d x} (3^{x}) = 3^{x} ln (3)

= 5 x^{4} \cdot 3^{x} + 3^{x} ln (3) x^{5}

- \frac{1}{x ^{2}} + sec^{2} (x)

x \to 1 + lim (\frac{3 x}{x ^{2} - 1})

\int (1 + (\frac{1}{4 x ^{\frac{2}{3}}})) d x

\frac{d y}{d x} = 2 y - 2 y^{5}

n = 0 \sum \infty \frac{1}{( n + 1 ) ^{2}}

What is the derivative of y=x^53^x ?
The derivative of y=x^53^x is 5x^4*3^x+3^xln(3)x^5
What is the first derivative of y=x^53^x ?
The first derivative of y=x^53^x is 5x^4*3^x+3^xln(3)x^5