What is the derivative of (9x^2-15xe^x) ?

The derivative of (9x^2-15xe^x) is 9e^xx^2+3e^xx-15e^x

What is the first derivative of (9x^2-15xe^x) ?

The first derivative of (9x^2-15xe^x) is 9e^xx^2+3e^xx-15e^x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} ((9 x^{2} - 15 x) e^{x})

9 e^{x} x^{2} + 3 e^{x} x - 15 e^{x}

Solution steps

\frac{d}{d x} ((9 x^{2} - 15 x) e^{x})

Apply the Product Rule:

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

f = 9 x^{2} - 15 x, g = e^{x}

= \frac{d}{d x} (9 x^{2} - 15 x) e^{x} + \frac{d}{d x} (e^{x}) (9 x^{2} - 15 x)

\frac{d}{d x} (9 x^{2} - 15 x) = 18 x - 15

\frac{d}{d x} (e^{x}) = e^{x}

= (18 x - 15) e^{x} + e^{x} (9 x^{2} - 15 x)

Simplify

(18 x - 15) e^{x} + e^{x} (9 x^{2} - 15 x) : 9 e^{x} x^{2} + 3 e^{x} x - 15 e^{x}

= 9 e^{x} x^{2} + 3 e^{x} x - 15 e^{x}

\frac{d}{d x} ((x e^{x})^{π})

\int \frac{e ^{x}}{3 + e ^{x}} d x

\int ln (13 t) d t

\int r^{2} (r^{3} - 2)^{2} d r

H (- 5) = 2^{x}

What is the derivative of (9x^2-15xe^x) ?
The derivative of (9x^2-15xe^x) is 9e^xx^2+3e^xx-15e^x
What is the first derivative of (9x^2-15xe^x) ?
The first derivative of (9x^2-15xe^x) is 9e^xx^2+3e^xx-15e^x