What is the derivative of 0.9x^35^x ?

The derivative of 0.9x^35^x is 0.9(3*5^xx^2+1.60943…*5^xx^3)

What is the first derivative of 0.9x^35^x ?

The first derivative of 0.9x^35^x is 0.9(3*5^xx^2+1.60943…*5^xx^3)

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derivative of

0.9 x^{3} 5^{x}

0.9 (3 \cdot 5^{x} x^{2} + 1.60943 \dots \cdot 5^{x} x^{3})

Solution steps

\frac{d}{d x} (0.9 x^{3} \cdot 5^{x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 0.9 \frac{d}{d x} (x^{3} \cdot 5^{x})

Apply the Product Rule:

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

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

= 0.9 (\frac{d}{d x} (x^{3}) 5^{x} + \frac{d}{d x} (5^{x}) x^{3})

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

= 0.9 (3 x^{2} \cdot 5^{x} + 5^{x} ln (5) x^{3})

Refine to a decimal form

= 0.9 (3 \cdot 5^{x} x^{2} + 1.60943 \dots \cdot 5^{x} x^{3})

\int \frac{( 5 + ln ( x ) ) ^{\frac{2}{3}}}{x} d x

\frac{\partial}{\partial y} (x^{5 y})

\int (x^{5}) d x

\int sin (x + \frac{π}{4}) d x

\int_{2}^{\infty} e^{- 3 p} d p

What is the derivative of 0.9x^35^x ?
The derivative of 0.9x^35^x is 0.9(3*5^xx^2+1.60943…*5^xx^3)
What is the first derivative of 0.9x^35^x ?
The first derivative of 0.9x^35^x is 0.9(3*5^xx^2+1.60943…*5^xx^3)