Differentiëren

\(f'(a)=7⋅2⋅a^1+6\text{.}\)

\(f'(a)=14a+6\text{.}\)

\(f'(x)=4⋅9⋅x^8+9⋅8⋅x^7-4\text{.}\)

\(f'(x)=36x^8+72x^7-4\text{.}\)

\(f'(x)=\frac{1}{2}⋅9⋅x^8+2⋅8⋅x^7+1\frac{3}{5}⋅3⋅x^2+\frac{4}{7}⋅2⋅x^1\text{.}\)

\(f'(x)=4\frac{1}{2}x^8+16x^7+4\frac{4}{5}x^2+1\frac{1}{7}x\text{.}\)

(Haakjes wegwerken)
\(f(a)=(8a^3-1)(a-2)=8a^4-16a^3-a+2\)

(Differentiëren)
\(f'(a)=32a^3-48a^2-1\text{.}\)

(Haakjes wegwerken)
\(f(p)=(3p^2+4)^2=9p^4+24p^2+16\)

(Differentiëren)
\(f'(p)=36p^3+48p\text{.}\)

(Herleiden)
\(f(x)=-4x⋅\sqrt[9]{x^5}=-4⋅x^1⋅x^{\frac{5}{9}}=-4⋅x^{1\frac{5}{9}}\)

(Differentiëren)
\(f'(x)=-4⋅1\frac{5}{9}⋅x^{\frac{5}{9}}\)

(Herleiden)
\(f'(x)=-6\frac{2}{9}⋅x^0⋅x^{\frac{5}{9}}=-6\frac{2}{9}⋅\sqrt[9]{x^5}\)

(Herleiden)
\(f(p)={4 \over 5p^8}=\frac{4}{5}p^{-8}\)

(Differentiëren)
\(f'(p)=\frac{4}{5}⋅-8⋅p^{-9}=-\frac{32}{5}⋅p^{-9}\)

(Herleiden)
\(f'(p)=-\frac{32}{5}⋅{1 \over p^9}=-{32 \over 5p^9}\)

(Herleiden)
\(f(x)={2 \over 7\sqrt{x}}+4\sqrt{x}=\frac{2}{7}x^{-\frac{1}{2}}+4x^{\frac{1}{2}}\)

(Differentiëren)
\(f'(x)=\frac{2}{7}⋅-\frac{1}{2}⋅x^{-1\frac{1}{2}}+4⋅\frac{1}{2}⋅x^{-\frac{1}{2}}\)

(Herleiden)
\(f'(x)=-{1 \over 7x\sqrt{x}}+{2 \over \sqrt{x}}\)

(Uitdelen)
\(f(a)={a^7 \over 3a^4}+{5a^3 \over 3a^4}=\frac{1}{3}a^3+\frac{5}{3}a^{-1}\)

(Differentiëren)
\(f'(a)=\frac{1}{3}⋅3⋅a^2+\frac{5}{3}⋅-1⋅a^{-2}\)

(Herleiden)
\(f'(a)=a^2-{5 \over 3a^2}\)

(Herleiden)
\(f(a)={4a^2+3 \over a^{\frac{1}{5}}}\)

(Uitdelen)
\(f(a)={4a^2 \over a^{\frac{1}{5}}}+{3 \over a^{\frac{1}{5}}}=4a^{1\frac{4}{5}}+3a^{-\frac{1}{5}}\)

(Differentiëren)
\(f'(a)=4⋅1\frac{4}{5}⋅a^{\frac{4}{5}}+3⋅-\frac{1}{5}⋅a^{-1\frac{1}{5}}\)

(Herleiden)
\(f'(a)=7\frac{1}{5}⋅\sqrt[5]{a^4}-{3 \over 5a⋅\sqrt[5]{a}}\)

(Herleiden)
\(f(x)={x+5 \over x^{2\frac{1}{2}}}\)

(Uitdelen)
\(f(x)={x \over x^{2\frac{1}{2}}}+{5 \over x^{2\frac{1}{2}}}=x^{-1\frac{1}{2}}+5x^{-2\frac{1}{2}}\)

(Differentiëren)
\(f'(x)=-1\frac{1}{2}⋅x^{-2\frac{1}{2}}+5⋅-2\frac{1}{2}⋅x^{-3\frac{1}{2}}\)

(Herleiden)
\(f'(x)=-{3 \over 2x^2⋅\sqrt{x}}-{25 \over 2x^3⋅\sqrt{x}}\)

(Quotiëntregel)
\(f'(p)={(-3p+9)⋅-2-(-2p+8)⋅-3 \over (-3p+9)^2}\text{.}\)

\(f'(p)={(6p-18)-(6p-24) \over (-3p+9)^2}={6 \over (-3p+9)^2}\text{.}\)

(Quotiëntregel)
\(f'(a)={(a-2)⋅-8a--4a^2⋅1 \over (a-2)^2}\text{.}\)

\(f'(a)={(-8a^2+16a)--4a^2 \over (a-2)^2}={-4a^2+16a \over (a-2)^2}\text{.}\)

(Kettingregel)
\(f'(a)=6⋅5⋅(2a+9)^4⋅2\)

(Herleiden)
\(f'(a)=60(2a+9)^4\text{.}\)

(Kettingregel)
\(f'(x)=6⋅3⋅(x^4+2x^3+5x^2)^2⋅(4x^3+6x^2+10x)\)

(Herleiden)
\(f'(x)=(72x^3+108x^2+180x)⋅(x^4+2x^3+5x^2)^2\)

(Herleiden)
\(f(a)=-{1 \over (4a-5)^3}=-1⋅(4a-5)^{-3}\)

(Kettingregel)
\(f'(a)=-1⋅-3⋅(4a-5)^{-4}⋅4\)

(Herleiden)
\(f'(a)=12⋅(4a-5)^{-4}={12 \over (4a-5)^4}\)

(Herleiden)
\(f(p)=2\sqrt{5p+4}=2⋅(5p+4)^{\frac{1}{2}}\text{.}\)

(Kettingregel)
\(f'(p)=2⋅\frac{1}{2}⋅(5p+4)^{-\frac{1}{2}}⋅5\)

(Herleiden)
\(f'(p)=5⋅(5p+4)^{-\frac{1}{2}}={5 \over \sqrt{5p+4}}\)

(Herleiden)
\(f(x)=-{9 \over 4\sqrt{4x+3}}=-\frac{9}{4}⋅(4x+3)^{-\frac{1}{2}}\)

(Kettingregel)
\(f'(x)=-\frac{9}{4}⋅-\frac{1}{2}⋅(4x+3)^{-1\frac{1}{2}}⋅4\)

(Herleiden)
\(f'(x)=\frac{9}{2}⋅(4x+3)^{-1\frac{1}{2}}={9 \over 2(4x+3)\sqrt{4x+3}}\)

\(f(x)=4⋅3^{x^3+2}⋅\ln(3)⋅3x^2=12x^2⋅3^{x^3+2}⋅\ln(3)\)

\(f(a)=(-10a-4)⋅e^{a-2}+(-5a^2-4a)⋅e^{a-2}⋅1\)
\(\text{ }=(-10a-4)⋅e^{a-2}+(-5a^2-4a)⋅e^{a-2}\)
\(\text{ }=(-5a^2-14a-4)⋅e^{a-2}\)

(Productregel)
\(f'(x)=-8(6x^2+4x)+(-8x-4)(12x+4)\text{.}\)

(Productregel)
\(f'(a)=(16a-9)(-6a^2+a-2)+(8a^2-9a)(-12a+1)\text{.}\)